
"""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						( snake_case_     ):
     lowercase		  =		42
     lowercase		  =		None






def 				A		(							snake_case :int							,   snake_case :str=0.999							,   snake_case :Optional[int]="cosine"							,   ) ->      Dict:
 if alpha_transform_type == "cosine":

  def alpha_bar_fn(snake_case :List[str]						):
   return math.cos((t + 0.008) / 1.008 * math.pi / 2						) ** 2

 elif alpha_transform_type == "exp":

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

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

 __UpperCamelCase							    =			[]
 for i in range(_lowerCamelCase						):
  __UpperCamelCase							    =			i / num_diffusion_timesteps
  __UpperCamelCase							    =			(i + 1) / num_diffusion_timesteps
  betas.append(min(1 - alpha_bar_fn(_lowerCamelCase						) / alpha_bar_fn(_lowerCamelCase						)							,   _lowerCamelCase						)						)
 return torch.tensor(_lowerCamelCase							,   dtype=torch.floataa						)





class __lowerCAmelCase						( snake_case_     ,    snake_case_     ):
     lowercase		  =		[e.name for e in KarrasDiffusionSchedulers]
     lowercase		  =		1





     @register_to_config
     def __init__(      self      ,	__UpperCAmelCase = 1000      ,	__UpperCAmelCase = 0.0_0_0_1      ,	__UpperCAmelCase = 0.0_2      ,	__UpperCAmelCase = "linear"      ,	__UpperCAmelCase = None      ,	__UpperCAmelCase = False      ,	__UpperCAmelCase = "epsilon"      ,	__UpperCAmelCase = "linspace"      ,	__UpperCAmelCase = 0      ,	):

      '''simple docstring'''




      if trained_betas is not None:
       __UpperCamelCase							    =			torch.tensor(lowerCamelCase_      ,	dtype=torch.floataa )
      elif beta_schedule == "linear":
       __UpperCamelCase							    =			torch.linspace(lowerCamelCase_      ,	lowerCamelCase_      ,	lowerCamelCase_      ,	dtype=torch.floataa )
      elif beta_schedule == "scaled_linear":
       # this schedule is very specific to the latent diffusion model.
       __UpperCamelCase							    =			(
           torch.linspace(beta_start**0.5      ,	beta_end**0.5      ,	lowerCamelCase_      ,	dtype=torch.floataa ) ** 2
       )
      elif beta_schedule == "squaredcos_cap_v2":
       # Glide cosine schedule
       __UpperCamelCase							    =			betas_for_alpha_bar(lowerCamelCase_ )
      else:
       raise NotImplementedError(F'{beta_schedule} does is not implemented for {self.__class__}' )

      __UpperCamelCase							    =			1.0 - self.betas
      __UpperCamelCase							    =			torch.cumprod(self.alphas      ,	dim=0 )

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

      # setable values
      __UpperCamelCase							    =			None
      __UpperCamelCase							    =			use_karras_sigmas
      self.set_timesteps(lowerCamelCase_      ,	lowerCamelCase_ )
      __UpperCamelCase							    =			[]
      __UpperCamelCase							    =			False





     @property
     def 		UpperCAmelCase   (      self ):

      '''simple docstring'''




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

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





     def 		UpperCAmelCase   (      self      ,	__UpperCAmelCase      ,	__UpperCAmelCase ):

      '''simple docstring'''




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





     def 		UpperCAmelCase   (      self      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	__UpperCAmelCase ):

      '''simple docstring'''




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

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

      return integrated_coeff





     def 		UpperCAmelCase   (      self      ,	__UpperCAmelCase      ,	__UpperCAmelCase = None ):

      '''simple docstring'''




      __UpperCamelCase							    =			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":
       __UpperCamelCase							    =			np.linspace(0      ,	self.config.num_train_timesteps - 1      ,	lowerCamelCase_      ,	dtype=lowerCamelCase_ )[
           ::-1
       ].copy()
      elif self.config.timestep_spacing == "leading":
       __UpperCamelCase							    =			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
       __UpperCamelCase							    =			(np.arange(0      ,	lowerCamelCase_ ) * step_ratio).round()[::-1].copy().astype(lowerCamelCase_ )
       timesteps += self.config.steps_offset
      elif self.config.timestep_spacing == "trailing":
       __UpperCamelCase							    =			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
       __UpperCamelCase							    =			(np.arange(self.config.num_train_timesteps      ,	0      ,	-step_ratio )).round().copy().astype(lowerCamelCase_ )
       timesteps -= 1
      else:
       raise ValueError(
           F'{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.' )

      __UpperCamelCase							    =			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 )
      __UpperCamelCase							    =			np.log(lowerCamelCase_ )
      __UpperCamelCase							    =			np.interp(lowerCamelCase_      ,	np.arange(0      ,	len(lowerCamelCase_ ) )      ,	lowerCamelCase_ )

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

      __UpperCamelCase							    =			np.concatenate([sigmas, [0.0]] ).astype(np.floataa )

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

      __UpperCamelCase							    =			[]





     def 		UpperCAmelCase   (      self      ,	__UpperCAmelCase      ,	__UpperCAmelCase ):

      '''simple docstring'''




      __UpperCamelCase							    =			np.log(lowerCamelCase_ )

      # get distribution
      __UpperCamelCase							    =			log_sigma - log_sigmas[:, np.newaxis]

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

      __UpperCamelCase							    =			log_sigmas[low_idx]
      __UpperCamelCase							    =			log_sigmas[high_idx]

      # interpolate sigmas
      __UpperCamelCase							    =			(low - log_sigma) / (low - high)
      __UpperCamelCase							    =			np.clip(lowerCamelCase_      ,	0      ,	1 )

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





     def 		UpperCAmelCase   (      self      ,	__UpperCAmelCase ):

      '''simple docstring'''




      __UpperCamelCase							    =			in_sigmas[-1].item()
      __UpperCamelCase							    =			in_sigmas[0].item()

      __UpperCamelCase							    =			7.0  # 7.0 is the value used in the paper
      __UpperCamelCase							    =			np.linspace(0      ,	1      ,	self.num_inference_steps )
      __UpperCamelCase							    =			sigma_min ** (1 / rho)
      __UpperCamelCase							    =			sigma_max ** (1 / rho)
      __UpperCamelCase							    =			(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
      return sigmas





     def 		UpperCAmelCase   (      self      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	__UpperCAmelCase = 4      ,	__UpperCAmelCase = 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(lowerCamelCase_      ,	torch.Tensor ):
       __UpperCamelCase							    =			timestep.to(self.timesteps.device )
      __UpperCamelCase							    =			(self.timesteps == timestep).nonzero().item()
      __UpperCamelCase							    =			self.sigmas[step_index]

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

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

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

      if not return_dict:
       return (prev_sample,)

      return LMSDiscreteSchedulerOutput(prev_sample=lowerCamelCase_      ,	pred_original_sample=lowerCamelCase_ )





     def 		UpperCAmelCase   (      self      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	):

      '''simple docstring'''




      __UpperCamelCase							    =			self.sigmas.to(device=original_samples.device      ,	dtype=original_samples.dtype )
      if original_samples.device.type == "mps" and torch.is_floating_point(lowerCamelCase_ ):
       # mps does not support float64
       __UpperCamelCase							    =			self.timesteps.to(original_samples.device      ,	dtype=torch.floataa )
       __UpperCamelCase							    =			timesteps.to(original_samples.device      ,	dtype=torch.floataa )
      else:
       __UpperCamelCase							    =			self.timesteps.to(original_samples.device )
       __UpperCamelCase							    =			timesteps.to(original_samples.device )

      __UpperCamelCase							    =			[(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

      __UpperCamelCase							    =			original_samples + noise * sigma
      return noisy_samples







     def __len__(      self ):

      '''simple docstring'''




      return self.config.num_train_timesteps











"""simple docstring"""
from __future__ import annotations






def 			lowerCamelCase_    (		_lowerCamelCase							):
 lowerCamelCase__	:     int
 lowerCamelCase__	:     list[str]								=		list(_lowerCamelCase							)
 lowerCamelCase__							,	lowerCamelCase__	:     Union[str, Any]								=		_vector[:-1], int(_vector[-1]							)
 lowerCamelCase__	:     list[int]								=		[int(_lowerCamelCase							) for digit in __vector]

 vector.reverse()
 for i, digit in enumerate(_lowerCamelCase							):
  if i & 1 == 0:
   lowerCamelCase__	:     int								=		digit * 2
   if doubled > 9:
    doubled -= 9
   check_digit += doubled
  else:
   check_digit += digit

 return check_digit % 10 == 0


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      assert is_luhn("79927398713")
      assert not is_luhn("79927398714")

