




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 							__SCREAMING_SNAKE_CASE				(						lowerCamelCase    ):
					_lowerCamelCase						    =					42
					_lowerCamelCase						    =					None






def    snake_case   (				A		,  A=0.999		,  A="cosine"		,  )				->				Tuple:




	'''simple docstring'''


	if alpha_transform_type == "cosine":

		def alpha_bar_fn(A     ):
			return math.cos((t + 0.008) / 1.008 * math.pi / 2     ) ** 2

	elif alpha_transform_type == "exp":

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

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

	lowerCamelCase_				:						Union[str, Any]				  =				[]
	for i in range(A     ):
		lowerCamelCase_				:						List[Any]				  =				i / num_diffusion_timesteps
		lowerCamelCase_				:						List[str]				  =				(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				(						lowerCamelCase  ,	lowerCamelCase    ):
					_lowerCamelCase						    =					[e.name for e in KarrasDiffusionSchedulers]
					_lowerCamelCase						    =					1

					@register_to_config
					def __init__(							self					,			__lowercase = 1_000					,			__lowercase = 0.00_01					,			__lowercase = 0.02					,			__lowercase = "linear"					,			__lowercase = None					,			__lowercase = False					,			__lowercase = "epsilon"					,			__lowercase = "linspace"					,			__lowercase = 0					,			):







						'''simple docstring'''




						if trained_betas is not None:
							lowerCamelCase_				:						Any				  =				torch.tensor(__lowercase					,			dtype=torch.floataa   )
						elif beta_schedule == "linear":
							lowerCamelCase_				:						Optional[Any]				  =				torch.linspace(__lowercase					,			__lowercase					,			__lowercase					,			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					,			__lowercase					,			dtype=torch.floataa   ) ** 2
							)
						elif beta_schedule == "squaredcos_cap_v2":
							# Glide cosine schedule
							lowerCamelCase_				:						Dict				  =				betas_for_alpha_bar(__lowercase   )
						else:
							raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}"   )

						lowerCamelCase_				:						Tuple				  =				1.0 - self.betas
						lowerCamelCase_				:						int				  =				torch.cumprod(self.alphas					,			dim=0   )

						lowerCamelCase_				:						Dict				  =				np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5   )
						lowerCamelCase_				:						Any				  =				np.concatenate([sigmas[::-1], [0.0]]   ).astype(np.floataa   )
						lowerCamelCase_				:						List[Any]				  =				torch.from_numpy(__lowercase   )

						# setable values
						lowerCamelCase_				:						Optional[int]				  =				None
						lowerCamelCase_				:						Dict				  =				use_karras_sigmas
						self.set_timesteps(__lowercase					,			__lowercase   )
						lowerCamelCase_				:						List[Any]				  =				[]
						lowerCamelCase_				:						Optional[int]				  =				False

					@property
					def       lowercase_				(							self   ):







						'''simple docstring'''




						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   ):







						'''simple docstring'''




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

					def       lowercase_				(							self					,			__lowercase					,			__lowercase					,			__lowercase   ):







						'''simple docstring'''




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

						lowerCamelCase_				:						Optional[Any]				  =				integrate.quad(__lowercase					,			self.sigmas[t]					,			self.sigmas[t + 1]					,			epsrel=1E-4   )[0]

						return integrated_coeff

					def       lowercase_				(							self					,			__lowercase					,			__lowercase = None   ):







						'''simple docstring'''




						lowerCamelCase_				:						Any				  =				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					,			__lowercase					,			dtype=__lowercase   )[
							    ::-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_				:						Tuple				  =				(np.arange(0					,			__lowercase   ) * step_ratio).round()[::-1].copy().astype(__lowercase   )
							timesteps += self.config.steps_offset
						elif self.config.timestep_spacing == "trailing":
							lowerCamelCase_				:						Union[str, 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(self.config.num_train_timesteps					,			0					,			-step_ratio   )).round().copy().astype(__lowercase   )
							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_				:						Optional[int]				  =				np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5   )
						lowerCamelCase_				:						List[str]				  =				np.log(__lowercase   )
						lowerCamelCase_				:						Optional[Any]				  =				np.interp(__lowercase					,			np.arange(0					,			len(__lowercase   )   )					,			__lowercase   )

						if self.use_karras_sigmas:
							lowerCamelCase_				:						Dict				  =				self._convert_to_karras(in_sigmas=__lowercase   )
							lowerCamelCase_				:						int				  =				np.array([self._sigma_to_t(__lowercase					,			__lowercase   ) for sigma in sigmas]   )

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

						lowerCamelCase_				:						str				  =				torch.from_numpy(__lowercase   ).to(device=__lowercase   )
						if str(__lowercase   ).startswith('mps'   ):
							# mps does not support float64
							lowerCamelCase_				:						Union[str, Any]				  =				torch.from_numpy(__lowercase   ).to(__lowercase					,			dtype=torch.floataa   )
						else:
							lowerCamelCase_				:						Optional[Any]				  =				torch.from_numpy(__lowercase   ).to(device=__lowercase   )

						lowerCamelCase_				:						Tuple				  =				[]

					def       lowercase_				(							self					,			__lowercase					,			__lowercase   ):







						'''simple docstring'''




						lowerCamelCase_				:						str				  =				np.log(__lowercase   )

						# get distribution
						lowerCamelCase_				:						Union[str, Any]				  =				log_sigma - log_sigmas[:, np.newaxis]

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

						lowerCamelCase_				:						Dict				  =				log_sigmas[low_idx]
						lowerCamelCase_				:						List[Any]				  =				log_sigmas[high_idx]

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

						# transform interpolation to time range
						lowerCamelCase_				:						Tuple				  =				(1 - w) * low_idx + w * high_idx
						lowerCamelCase_				:						Dict				  =				t.reshape(sigma.shape   )
						return t

					def       lowercase_				(							self					,			__lowercase   ):







						'''simple docstring'''




						lowerCamelCase_				:						float				  =				in_sigmas[-1].item()
						lowerCamelCase_				:						float				  =				in_sigmas[0].item()

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

					def       lowercase_				(							self					,			__lowercase					,			__lowercase					,			__lowercase					,			__lowercase = 4					,			__lowercase = True					,			):







						'''simple docstring'''




						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(__lowercase					,			torch.Tensor   ):
							lowerCamelCase_				:						List[Any]				  =				timestep.to(self.timesteps.device   )
						lowerCamelCase_				:						Union[str, Any]				  =				(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_				:						int				  =				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_				:						Tuple				  =				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_				:						int				  =				(sample - pred_original_sample) / sigma
						self.derivatives.append(__lowercase   )
						if len(self.derivatives   ) > order:
							self.derivatives.pop(0   )

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

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

						if not return_dict:
							return (prev_sample,)

						return LMSDiscreteSchedulerOutput(prev_sample=__lowercase					,			pred_original_sample=__lowercase   )

					def       lowercase_				(							self					,			__lowercase					,			__lowercase					,			__lowercase					,			):







						'''simple docstring'''




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

						lowerCamelCase_				:						Union[str, Any]				  =				[(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

						lowerCamelCase_				:						str				  =				original_samples + noise * sigma
						return noisy_samples





					def __len__(							self   ):







						'''simple docstring'''




						return self.config.num_train_timesteps








from collections import namedtuple

UpperCamelCase											=      namedtuple('''from_to''', '''from_ to''')

UpperCamelCase											=      {
    '''millimeter''': '''mm''',
    '''centimeter''': '''cm''',
    '''meter''': '''m''',
    '''kilometer''': '''km''',
    '''inch''': '''in''',
    '''inche''': '''in''',  # Trailing 's' has been stripped off
    '''feet''': '''ft''',
    '''foot''': '''ft''',
    '''yard''': '''yd''',
    '''mile''': '''mi''',
}

UpperCamelCase											=      {
    '''mm''': from_to(0.001, 1_0_0_0),
    '''cm''': from_to(0.01, 1_0_0),
    '''m''': from_to(1, 1),
    '''km''': from_to(1_0_0_0, 0.001),
    '''in''': from_to(0.0254, 39.3701),
    '''ft''': from_to(0.3048, 3.2_8084),
    '''yd''': from_to(0.9144, 1.0_9361),
    '''mi''': from_to(1609.34, 0.0_0062_1371),
}




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      float:
 lowerCamelCase_							:    List[Any]							=     from_type.lower().rstrip('s'				)
 lowerCamelCase_							:    Optional[Any]							=     TYPE_CONVERSION.get(lowerCamelCase__ ,			lowerCamelCase__				)
 lowerCamelCase_							:    List[Any]							=     to_type.lower().rstrip('s'				)
 lowerCamelCase_							:    Optional[int]							=     TYPE_CONVERSION.get(lowerCamelCase__ ,			lowerCamelCase__				)
 if new_from not in METRIC_CONVERSION:
  lowerCamelCase_							:    List[Any]							=     (
      F'Invalid \'from_type\' value: {from_type!r}.\n'
      F'Conversion abbreviations are: {", ".join(lowerCamelCase__				)}'
  )
  raise ValueError(lowerCamelCase__				)
 if new_to not in METRIC_CONVERSION:
  lowerCamelCase_							:    List[str]							=     (
      F'Invalid \'to_type\' value: {to_type!r}.\n'
      F'Conversion abbreviations are: {", ".join(lowerCamelCase__				)}'
  )
  raise ValueError(lowerCamelCase__				)
 return value * METRIC_CONVERSION[new_from].from_ * METRIC_CONVERSION[new_to].to


if __name__ == "__main__":
       import doctest

       doctest.testmod()
