





import math
import warnings
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class 							snake_case_		(      lowercase_):
		lowerCamelCase     :torch.FloatTensor
		lowerCamelCase     :Optional[torch.FloatTensor]							=  None


def        A__						(							SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_=0.9_9_9				,							SCREAMING_SNAKE_CASE_="cosine"				,							) ->  str:
		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 :			List[Any]    		=i / num_diffusion_timesteps
				lowerCamelCase :			Optional[int]    		=(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     :List[Any]							=  [e.name for e in KarrasDiffusionSchedulers]
		lowerCamelCase     :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 = None      ,  __lowercase = False      ,  __lowercase = "epsilon"      ,  __lowercase = "linspace"      ,  __lowercase = 0      ,  )					-> str:







				if trained_betas is not None:
						lowerCamelCase :			Any    		=torch.tensor(UpperCAmelCase_      ,  dtype=torch.floataa )
				elif beta_schedule == "linear":
						lowerCamelCase :			str    		=torch.linspace(UpperCAmelCase_      ,  UpperCAmelCase_      ,  UpperCAmelCase_      ,  dtype=torch.floataa )
				elif beta_schedule == "scaled_linear":
						# this schedule is very specific to the latent diffusion model.
						lowerCamelCase :			Dict    		=(
						    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 :			Dict    		=betas_for_alpha_bar(UpperCAmelCase_ )
				else:
						raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}" )

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

				lowerCamelCase :			Any    		=np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 )
				lowerCamelCase :			Optional[Any]    		=np.concatenate([sigmas[::-1], [0.0]] ).astype(np.floataa )
				lowerCamelCase :			int    		=torch.from_numpy(UpperCAmelCase_ )

				# setable values
				lowerCamelCase :			List[str]    		=None
				lowerCamelCase :			Optional[Any]    		=use_karras_sigmas
				self.set_timesteps(UpperCAmelCase_      ,  UpperCAmelCase_ )
				lowerCamelCase :			int    		=[]
				lowerCamelCase :			int    		=False







		@property
		def       __lowercase (		self )					-> Dict:







				if self.config.timestep_spacing in ["linspace", "trailing"]:
						return self.sigmas.max()

				return (self.sigmas.max() ** 2 + 1) ** 0.5







		def       __lowercase (		self      ,  __lowercase      ,  __lowercase )					-> torch.FloatTensor:







				if isinstance(UpperCAmelCase_      ,  torch.Tensor ):
						lowerCamelCase :			Union[str, Any]    		=timestep.to(self.timesteps.device )
				lowerCamelCase :			Union[str, Any]    		=(self.timesteps == timestep).nonzero().item()
				lowerCamelCase :			Optional[Any]    		=self.sigmas[step_index]
				lowerCamelCase :			Optional[int]    		=sample / ((sigma**2 + 1) ** 0.5)
				lowerCamelCase :			Any    		=True
				return sample







		def       __lowercase (		self      ,  __lowercase      ,  __lowercase      ,  __lowercase )					-> Tuple:







				def lms_derivative(__lowercase ):
						lowerCamelCase :			str    		=1.0
						for k in range(UpperCAmelCase_ ):
								if current_order == k:
										continue
								prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
						return prod

				lowerCamelCase :			Union[str, Any]    		=integrate.quad(UpperCAmelCase_      ,  self.sigmas[t]      ,  self.sigmas[t + 1]      ,  epsrel=1e-4 )[0]

				return integrated_coeff







		def       __lowercase (		self      ,  __lowercase      ,  __lowercase = None )					-> Union[str, Any]:
				lowerCamelCase :			int    		=num_inference_steps

				# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
				if self.config.timestep_spacing == "linspace":
						lowerCamelCase :			int    		=np.linspace(0      ,  self.config.num_train_timesteps - 1      ,  UpperCAmelCase_      ,  dtype=UpperCAmelCase_ )[
						    ::-1
						].copy()
				elif self.config.timestep_spacing == "leading":
						lowerCamelCase :			List[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
						lowerCamelCase :			List[str]    		=(np.arange(0      ,  UpperCAmelCase_ ) * step_ratio).round()[::-1].copy().astype(UpperCAmelCase_ )
						timesteps += self.config.steps_offset
				elif self.config.timestep_spacing == "trailing":
						lowerCamelCase :			List[str]    		=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 :			int    		=(np.arange(self.config.num_train_timesteps      ,  0      ,  -step_ratio )).round().copy().astype(UpperCAmelCase_ )
						timesteps -= 1
				else:
						raise ValueError(
						    F"{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'." )

				lowerCamelCase :			List[str]    		=np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 )
				lowerCamelCase :			List[Any]    		=np.log(UpperCAmelCase_ )
				lowerCamelCase :			List[Any]    		=np.interp(UpperCAmelCase_      ,  np.arange(0      ,  len(UpperCAmelCase_ ) )      ,  UpperCAmelCase_ )

				if self.use_karras_sigmas:
						lowerCamelCase :			Optional[int]    		=self._convert_to_karras(in_sigmas=UpperCAmelCase_ )
						lowerCamelCase :			List[Any]    		=np.array([self._sigma_to_t(UpperCAmelCase_      ,  UpperCAmelCase_ ) for sigma in sigmas] )

				lowerCamelCase :			Dict    		=np.concatenate([sigmas, [0.0]] ).astype(np.floataa )

				lowerCamelCase :			str    		=torch.from_numpy(UpperCAmelCase_ ).to(device=UpperCAmelCase_ )
				if str(UpperCAmelCase_ ).startswith('''mps''' ):
						# mps does not support float64
						lowerCamelCase :			Any    		=torch.from_numpy(UpperCAmelCase_ ).to(UpperCAmelCase_      ,  dtype=torch.floataa )
				else:
						lowerCamelCase :			str    		=torch.from_numpy(UpperCAmelCase_ ).to(device=UpperCAmelCase_ )

				lowerCamelCase :			List[Any]    		=[]







		def       __lowercase (		self      ,  __lowercase      ,  __lowercase )					-> List[Any]:
				lowerCamelCase :			Tuple    		=np.log(UpperCAmelCase_ )

				# get distribution
				lowerCamelCase :			List[str]    		=log_sigma - log_sigmas[:, np.newaxis]

				# get sigmas range
				lowerCamelCase :			List[str]    		=np.cumsum((dists >= 0)      ,  axis=0 ).argmax(axis=0 ).clip(max=log_sigmas.shape[0] - 2 )
				lowerCamelCase :			Tuple    		=low_idx + 1

				lowerCamelCase :			Optional[Any]    		=log_sigmas[low_idx]
				lowerCamelCase :			Optional[int]    		=log_sigmas[high_idx]

				# interpolate sigmas
				lowerCamelCase :			Optional[int]    		=(low - log_sigma) / (low - high)
				lowerCamelCase :			Optional[int]    		=np.clip(UpperCAmelCase_      ,  0      ,  1 )

				# transform interpolation to time range
				lowerCamelCase :			List[str]    		=(1 - w) * low_idx + w * high_idx
				lowerCamelCase :			Union[str, Any]    		=t.reshape(sigma.shape )
				return t







		def       __lowercase (		self      ,  __lowercase )					-> torch.FloatTensor:
				lowerCamelCase :			float    		=in_sigmas[-1].item()
				lowerCamelCase :			float    		=in_sigmas[0].item()

				lowerCamelCase :			Dict    		=7.0  # 7.0 is the value used in the paper
				lowerCamelCase :			Optional[Any]    		=np.linspace(0      ,  1      ,  self.num_inference_steps )
				lowerCamelCase :			List[Any]    		=sigma_min ** (1 / rho)
				lowerCamelCase :			Optional[int]    		=sigma_max ** (1 / rho)
				lowerCamelCase :			List[Any]    		=(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
				return sigmas







		def       __lowercase (		self      ,  __lowercase      ,  __lowercase      ,  __lowercase      ,  __lowercase = 4      ,  __lowercase = True      ,  )					-> Union[LMSDiscreteSchedulerOutput, Tuple]:







				if not self.is_scale_input_called:
						warnings.warn(
						    '''The `scale_model_input` function should be called before `step` to ensure correct denoising. '''
						    '''See `StableDiffusionPipeline` for a usage example.''' )

				if isinstance(UpperCAmelCase_      ,  torch.Tensor ):
						lowerCamelCase :			Union[str, Any]    		=timestep.to(self.timesteps.device )
				lowerCamelCase :			str    		=(self.timesteps == timestep).nonzero().item()
				lowerCamelCase :			Dict    		=self.sigmas[step_index]

				# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
				if self.config.prediction_type == "epsilon":
						lowerCamelCase :			Union[str, Any]    		=sample - sigma * model_output
				elif self.config.prediction_type == "v_prediction":
						# * c_out + input * c_skip
						lowerCamelCase :			Dict    		=model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
				elif self.config.prediction_type == "sample":
						lowerCamelCase :			str    		=model_output
				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
				lowerCamelCase :			Optional[Any]    		=(sample - pred_original_sample) / sigma
				self.derivatives.append(UpperCAmelCase_ )
				if len(self.derivatives ) > order:
						self.derivatives.pop(0 )

				# 3. Compute linear multistep coefficients
				lowerCamelCase :			Optional[Any]    		=min(step_index + 1      ,  UpperCAmelCase_ )
				lowerCamelCase :			List[Any]    		=[self.get_lms_coefficient(UpperCAmelCase_      ,  UpperCAmelCase_      ,  UpperCAmelCase_ ) for curr_order in range(UpperCAmelCase_ )]

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

				if not return_dict:
						return (prev_sample,)

				return LMSDiscreteSchedulerOutput(prev_sample=UpperCAmelCase_      ,  pred_original_sample=UpperCAmelCase_ )







		def       __lowercase (		self      ,  __lowercase      ,  __lowercase      ,  __lowercase      ,  )					-> torch.FloatTensor:
				lowerCamelCase :			Any    		=self.sigmas.to(device=original_samples.device      ,  dtype=original_samples.dtype )
				if original_samples.device.type == "mps" and torch.is_floating_point(UpperCAmelCase_ ):
						# mps does not support float64
						lowerCamelCase :			List[Any]    		=self.timesteps.to(original_samples.device      ,  dtype=torch.floataa )
						lowerCamelCase :			List[Any]    		=timesteps.to(original_samples.device      ,  dtype=torch.floataa )
				else:
						lowerCamelCase :			int    		=self.timesteps.to(original_samples.device )
						lowerCamelCase :			Tuple    		=timesteps.to(original_samples.device )

				lowerCamelCase :			Optional[int]    		=[(schedule_timesteps == t).nonzero().item() for t in timesteps]

				lowerCamelCase :			List[str]    		=sigmas[step_indices].flatten()
				while len(sigma.shape ) < len(original_samples.shape ):
						lowerCamelCase :			Dict    		=sigma.unsqueeze(-1 )

				lowerCamelCase :			Dict    		=original_samples + noise * sigma
				return noisy_samples







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






def 	_A	(   _UpperCamelCase			):
				if not isinstance(_UpperCamelCase      ,					_UpperCamelCase			):
								_UpperCAmelCase						:  List[Any]     					=	(
								    '''operation can not be conducted on a object of type '''
								    F'''{type(_UpperCamelCase			).__name__}'''
								)
								raise TypeError(_UpperCamelCase			)
				_UpperCAmelCase						:  List[str]     					=	''''''
				for _ in range(0      ,					32			):
								bit_string += str(number % 2			)
								_UpperCAmelCase						:  Union[str, Any]     					=	number >> 1
				return bit_string


def 	_A	(   _UpperCamelCase			):
				if number < 0:
								raise ValueError('''the value of input must be positive'''			)
				elif isinstance(_UpperCamelCase      ,					_UpperCamelCase			):
								raise TypeError('''Input value must be a \'int\' type'''			)
				elif isinstance(_UpperCamelCase      ,					_UpperCamelCase			):
								raise TypeError('''\'<\' not supported between instances of \'str\' and \'int\''''			)
				_UpperCAmelCase						:  Tuple     					=	0
				# iterator over [1 to 32],since we are dealing with 32 bit integer
				for _ in range(1      ,					33			):
								# left shift the bits by unity
								_UpperCAmelCase						:  List[str]     					=	result << 1
								# get the end bit
								_UpperCAmelCase						:  List[Any]     					=	number % 2
								# right shift the bits by unity
								_UpperCAmelCase						:  Optional[int]     					=	number >> 1
								# add that bit to our ans
								_UpperCAmelCase						:  Any     					=	result | end_bit
				return get_reverse_bit_string(_UpperCamelCase			)


if __name__ == "__main__":
					import doctest

					doctest.testmod()
