


'''simple docstring'''




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 			lowerCAmelCase					(					a				):
	_lowerCamelCase :       torch.FloatTensor
	_lowerCamelCase :       Optional[torch.FloatTensor]         =			None


def       __UpperCamelCase     (     _A     :					Optional[Any]       , _A     :					Optional[Any]=0.9_99       , _A     :					Union[str, Any]="cosine"       , )     ->   Union[str, Any]:




	"""simple docstring"""





	if alpha_transform_type == "cosine":

		def alpha_bar_fn(_A     :					List[Any]					):
			return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2					) ** 2

	elif alpha_transform_type == "exp":

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

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

	lowerCAmelCase       :     List[str]   				=			[]
	for i in range(_A					):
		lowerCAmelCase       :     Any   				=			i / num_diffusion_timesteps
		lowerCAmelCase       :     Optional[int]   				=			(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 			lowerCAmelCase					(					a   ,					a				):
	_lowerCamelCase :       Dict         =			[e.name for e in KarrasDiffusionSchedulers]
	_lowerCamelCase :       int         =			1



	@register_to_config
	def __init__(       self			,       snake_case__ = 1000			,       snake_case__ = 0.0_0_0_1			,       snake_case__ = 0.0_2			,       snake_case__ = "linear"			,       snake_case__ = None			,       snake_case__ = False			,       snake_case__ = "epsilon"			,       snake_case__ = "linspace"			,       snake_case__ = 0			,       ):
		if trained_betas is not None:
			lowerCAmelCase       :     List[str]   				=			torch.tensor(snake_case__			,       dtype=torch.floataa     )
		elif beta_schedule == "linear":
			lowerCAmelCase       :     List[str]   				=			torch.linspace(snake_case__			,       snake_case__			,       snake_case__			,       dtype=torch.floataa     )
		elif beta_schedule == "scaled_linear":
			# this schedule is very specific to the latent diffusion model.
			lowerCAmelCase       :     Tuple   				=			(
			    torch.linspace(beta_start**0.5			,       beta_end**0.5			,       snake_case__			,       dtype=torch.floataa     ) ** 2
			)
		elif beta_schedule == "squaredcos_cap_v2":
			# Glide cosine schedule
			lowerCAmelCase       :     Optional[Any]   				=			betas_for_alpha_bar(snake_case__     )
		else:
			raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}"     )

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

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

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



	@property
	def 					lowercase  (       self     ):
		# standard deviation of the initial noise distribution
		if self.config.timestep_spacing in ["linspace", "trailing"]:
			return self.sigmas.max()

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



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



	def 					lowercase  (       self			,       snake_case__			,       snake_case__			,       snake_case__     ):

		def lms_derivative(snake_case__     ):
			lowerCAmelCase       :     Any   				=			1.0
			for k in range(snake_case__     ):
				if current_order == k:
					continue
				prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
			return prod

		lowerCAmelCase       :     Any   				=			integrate.quad(snake_case__			,       self.sigmas[t]			,       self.sigmas[t + 1]			,       epsrel=1e-4     )[0]

		return integrated_coeff



	def 					lowercase  (       self			,       snake_case__			,       snake_case__ = None     ):
		lowerCAmelCase       :     Tuple   				=			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       :     Any   				=			np.linspace(0			,       self.config.num_train_timesteps - 1			,       snake_case__			,       dtype=snake_case__     )[
			    ::-1
			].copy()
		elif self.config.timestep_spacing == "leading":
			lowerCAmelCase       :     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       :     Union[str, Any]   				=			(np.arange(0			,       snake_case__     ) * step_ratio).round()[::-1].copy().astype(snake_case__     )
			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       :     List[Any]   				=			(np.arange(self.config.num_train_timesteps			,       0			,       -step_ratio     )).round().copy().astype(snake_case__     )
			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       :     str   				=			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5     )
		lowerCAmelCase       :     Tuple   				=			np.log(snake_case__     )
		lowerCAmelCase       :     List[Any]   				=			np.interp(snake_case__			,       np.arange(0			,       len(snake_case__     )     )			,       snake_case__     )

		if self.use_karras_sigmas:
			lowerCAmelCase       :     Optional[int]   				=			self._convert_to_karras(in_sigmas=snake_case__     )
			lowerCAmelCase       :     Optional[int]   				=			np.array([self._sigma_to_t(snake_case__			,       snake_case__     ) for sigma in sigmas]     )

		lowerCAmelCase       :     Any   				=			np.concatenate([sigmas, [0.0]]     ).astype(np.floataa     )

		lowerCAmelCase       :     List[Any]   				=			torch.from_numpy(snake_case__     ).to(device=snake_case__     )
		if str(snake_case__     ).startswith('mps'     ):
			# mps does not support float64
			lowerCAmelCase       :     Tuple   				=			torch.from_numpy(snake_case__     ).to(snake_case__			,       dtype=torch.floataa     )
		else:
			lowerCAmelCase       :     Optional[Any]   				=			torch.from_numpy(snake_case__     ).to(device=snake_case__     )

		lowerCAmelCase       :     Tuple   				=			[]



	def 					lowercase  (       self			,       snake_case__			,       snake_case__     ):
		# get log sigma
		lowerCAmelCase       :     List[str]   				=			np.log(snake_case__     )

		# get distribution
		lowerCAmelCase       :     Optional[int]   				=			log_sigma - log_sigmas[:, np.newaxis]

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

		lowerCAmelCase       :     List[Any]   				=			log_sigmas[low_idx]
		lowerCAmelCase       :     Optional[int]   				=			log_sigmas[high_idx]

		# interpolate sigmas
		lowerCAmelCase       :     Optional[Any]   				=			(low - log_sigma) / (low - high)
		lowerCAmelCase       :     List[Any]   				=			np.clip(snake_case__			,       0			,       1     )

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



	def 					lowercase  (       self			,       snake_case__     ):
		lowerCAmelCase       :     float   				=			in_sigmas[-1].item()
		lowerCAmelCase       :     float   				=			in_sigmas[0].item()

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



	def 					lowercase  (       self			,       snake_case__			,       snake_case__			,       snake_case__			,       snake_case__ = 4			,       snake_case__ = True			,       ):
		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(snake_case__			,       torch.Tensor     ):
			lowerCAmelCase       :     Union[str, Any]   				=			timestep.to(self.timesteps.device     )
		lowerCAmelCase       :     Union[str, Any]   				=			(self.timesteps == timestep).nonzero().item()
		lowerCAmelCase       :     str   				=			self.sigmas[step_index]

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

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

		# 4. Compute previous sample based on the derivatives path
		lowerCAmelCase       :     List[Any]   				=			sample + sum(
		    coeff * derivative for coeff, derivative in zip(snake_case__			,       reversed(self.derivatives     )     )     )

		if not return_dict:
			return (prev_sample,)

		return LMSDiscreteSchedulerOutput(prev_sample=snake_case__			,       pred_original_sample=snake_case__     )



	def 					lowercase  (       self			,       snake_case__			,       snake_case__			,       snake_case__			,       ):
		# Make sure sigmas and timesteps have the same device and dtype as original_samples
		lowerCAmelCase       :     Dict   				=			self.sigmas.to(device=original_samples.device			,       dtype=original_samples.dtype     )
		if original_samples.device.type == "mps" and torch.is_floating_point(snake_case__     ):
			# mps does not support float64
			lowerCAmelCase       :     str   				=			self.timesteps.to(original_samples.device			,       dtype=torch.floataa     )
			lowerCAmelCase       :     Optional[int]   				=			timesteps.to(original_samples.device			,       dtype=torch.floataa     )
		else:
			lowerCAmelCase       :     Any   				=			self.timesteps.to(original_samples.device     )
			lowerCAmelCase       :     int   				=			timesteps.to(original_samples.device     )

		lowerCAmelCase       :     List[str]   				=			[(schedule_timesteps == t).nonzero().item() for t in timesteps]

		lowerCAmelCase       :     Optional[int]   				=			sigmas[step_indices].flatten()
		while len(sigma.shape     ) < len(original_samples.shape     ):
			lowerCAmelCase       :     Optional[int]   				=			sigma.unsqueeze(-1     )

		lowerCAmelCase       :     List[Any]   				=			original_samples + noise * sigma
		return noisy_samples



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




'''simple docstring'''




class 			lowerCAmelCase					:



	def __init__(       self			,       snake_case__     ):
		lowerCAmelCase       :     Dict   				=			data
		lowerCAmelCase       :     Dict   				=			None
		lowerCAmelCase       :     Optional[int]   				=			None



	def __str__(       self     ):
		return f"{self.data}"



class 			lowerCAmelCase					:



	def __init__(       self     ):
		lowerCAmelCase       :     int   				=			None
		lowerCAmelCase       :     Dict   				=			None



	def __iter__(       self     ):
		lowerCAmelCase       :     Any   				=			self.head
		while node:
			yield node.data
			lowerCAmelCase       :     Tuple   				=			node.next



	def __str__(       self     ):
		return "->".join([str(snake_case__     ) for item in self]     )



	def __len__(       self     ):
		return sum(1 for _ in self     )



	def 					lowercase  (       self			,       snake_case__     ):
		self.insert_at_nth(0			,       snake_case__     )



	def 					lowercase  (       self			,       snake_case__     ):
		self.insert_at_nth(len(self     )			,       snake_case__     )



	def 					lowercase  (       self			,       snake_case__			,       snake_case__     ):
		lowerCAmelCase       :     Dict   				=			len(self     )

		if not 0 <= index <= length:
			raise IndexError('list index out of range'     )
		lowerCAmelCase       :     Dict   				=			Node(snake_case__     )
		if self.head is None:
			lowerCAmelCase       :     Any   				=			new_node
		elif index == 0:
			lowerCAmelCase       :     Dict   				=			new_node
			lowerCAmelCase       :     List[str]   				=			self.head
			lowerCAmelCase       :     Any   				=			new_node
		elif index == length:
			lowerCAmelCase       :     List[str]   				=			new_node
			lowerCAmelCase       :     int   				=			self.tail
			lowerCAmelCase       :     List[str]   				=			new_node
		else:
			lowerCAmelCase       :     Optional[Any]   				=			self.head
			for _ in range(0			,       snake_case__     ):
				lowerCAmelCase       :     Dict   				=			temp.next
			lowerCAmelCase       :     Tuple   				=			new_node
			lowerCAmelCase       :     Union[str, Any]   				=			temp.previous
			lowerCAmelCase       :     int   				=			temp
			lowerCAmelCase       :     Optional[int]   				=			new_node



	def 					lowercase  (       self     ):
		return self.delete_at_nth(0     )



	def 					lowercase  (       self     ):
		return self.delete_at_nth(len(self     ) - 1     )



	def 					lowercase  (       self			,       snake_case__     ):
		lowerCAmelCase       :     Optional[Any]   				=			len(self     )

		if not 0 <= index <= length - 1:
			raise IndexError('list index out of range'     )
		lowerCAmelCase       :     List[Any]   				=			self.head  # default first node
		if length == 1:
			lowerCAmelCase       :     int   				=			None
		elif index == 0:
			lowerCAmelCase       :     str   				=			self.head.next
			lowerCAmelCase       :     Dict   				=			None
		elif index == length - 1:
			lowerCAmelCase       :     int   				=			self.tail
			lowerCAmelCase       :     Dict   				=			self.tail.previous
			lowerCAmelCase       :     str   				=			None
		else:
			lowerCAmelCase       :     str   				=			self.head
			for _ in range(0			,       snake_case__     ):
				lowerCAmelCase       :     Dict   				=			temp.next
			lowerCAmelCase       :     Tuple   				=			temp
			lowerCAmelCase       :     List[str]   				=			temp.previous
			lowerCAmelCase       :     Tuple   				=			temp.next
		return delete_node.data



	def 					lowercase  (       self			,       snake_case__     ):
		lowerCAmelCase       :     Dict   				=			self.head

		while current.data != data:  # Find the position to delete
			if current.next:
				lowerCAmelCase       :     str   				=			current.next
			else:  # We have reached the end an no value matches
				raise ValueError('No data matching given value'     )

		if current == self.head:
			self.delete_head()

		elif current == self.tail:
			self.delete_tail()

		else:  # Before: 1 <--> 2(current) <--> 3
			lowerCAmelCase       :     Optional[Any]   				=			current.next  # 1 --> 3
			lowerCAmelCase       :     str   				=			current.previous  # 1 <--> 3
		return data



	def 					lowercase  (       self     ):
		return len(self     ) == 0


def       __UpperCamelCase     (     )     ->   None:




	"""simple docstring"""





	lowerCAmelCase       :     str   				=			DoublyLinkedList()
	assert linked_list.is_empty() is True
	assert str(_A					) == ""

	try:
		linked_list.delete_head()
		raise AssertionError  # This should not happen.
	except IndexError:
		assert True  # This should happen.

	try:
		linked_list.delete_tail()
		raise AssertionError  # This should not happen.
	except IndexError:
		assert True  # This should happen.

	for i in range(10					):
		assert len(_A					) == i
		linked_list.insert_at_nth(_A       , i + 1					)
	assert str(_A					) == "->".join(str(_A					) for i in range(1       , 11					)					)

	linked_list.insert_at_head(0					)
	linked_list.insert_at_tail(11					)
	assert str(_A					) == "->".join(str(_A					) for i in range(0       , 12					)					)

	assert linked_list.delete_head() == 0
	assert linked_list.delete_at_nth(9					) == 10
	assert linked_list.delete_tail() == 11
	assert len(_A					) == 9
	assert str(_A					) == "->".join(str(_A					) for i in range(1       , 10					)					)


if __name__ == "__main__":
				from doctest import testmod

				testmod()
