






"""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 						a_ (      snake_case_					):







      '''simple docstring'''

      lowerCamelCase__			:							torch.FloatTensor
      lowerCamelCase__			:							Optional[torch.FloatTensor]					=      None






def 			lowerCamelCase_    (		_lowerCamelCase     ,  _lowerCamelCase=0.999     ,  _lowerCamelCase="cosine"     ,  ):
 if alpha_transform_type == "cosine":

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

 elif alpha_transform_type == "exp":

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

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

 lowerCamelCase__	:     Tuple								=		[]
 for i in range(_lowerCamelCase							):
  lowerCamelCase__	:     str								=		i / num_diffusion_timesteps
  lowerCamelCase__	:     Dict								=		(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 						a_ (      snake_case_    ,		snake_case_					):







      '''simple docstring'''

      lowerCamelCase__			:							Any					=      [e.name for e in KarrasDiffusionSchedulers]
      lowerCamelCase__			:							List[str]					=      1




      @register_to_config
      def __init__(self,	lowerCamelCase_ = 1_0_0_0,	lowerCamelCase_ = 0.0_001,	lowerCamelCase_ = 0.02,	lowerCamelCase_ = "linear",	lowerCamelCase_ = None,	lowerCamelCase_ = False,	lowerCamelCase_ = "epsilon",	lowerCamelCase_ = "linspace",	lowerCamelCase_ = 0,	):

       '''simple docstring'''



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

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

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

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




      @property
      def      a__				(self   ):

       '''simple docstring'''



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

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




      def      a__				(self,	lowerCamelCase_,	lowerCamelCase_   ):

       '''simple docstring'''



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




      def      a__				(self,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_   ):

       '''simple docstring'''



       def lms_derivative(lowerCamelCase_   ):
        lowerCamelCase__	:     Any								=		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

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

       return integrated_coeff




      def      a__				(self,	lowerCamelCase_,	lowerCamelCase_ = None   ):

       '''simple docstring'''



       lowerCamelCase__	:     Union[str, 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__	:     List[str]								=		np.linspace(0,	self.config.num_train_timesteps - 1,	lowerCamelCase_,	dtype=lowerCamelCase_   )[
            ::-1
        ].copy()
       elif self.config.timestep_spacing == "leading":
        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__	:     Optional[int]								=		(np.arange(0,	lowerCamelCase_   ) * step_ratio).round()[::-1].copy().astype(lowerCamelCase_   )
        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__	:     str								=		(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\'.'''   )

       lowerCamelCase__	:     Tuple								=		np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5   )
       lowerCamelCase__	:     Optional[int]								=		np.log(lowerCamelCase_   )
       lowerCamelCase__	:     Dict								=		np.interp(lowerCamelCase_,	np.arange(0,	len(lowerCamelCase_   )   ),	lowerCamelCase_   )

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

       lowerCamelCase__	:     int								=		np.concatenate([sigmas, [0.0]]   ).astype(np.floataa   )

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

       lowerCamelCase__	:     Union[str, Any]								=		[]




      def      a__				(self,	lowerCamelCase_,	lowerCamelCase_   ):

       '''simple docstring'''



       lowerCamelCase__	:     List[Any]								=		np.log(lowerCamelCase_   )

       # get distribution
       lowerCamelCase__	:     Union[str, Any]								=		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__	:     Dict								=		low_idx + 1

       lowerCamelCase__	:     Tuple								=		log_sigmas[low_idx]
       lowerCamelCase__	:     str								=		log_sigmas[high_idx]

       # interpolate sigmas
       lowerCamelCase__	:     Any								=		(low - log_sigma) / (low - high)
       lowerCamelCase__	:     Dict								=		np.clip(lowerCamelCase_,	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      a__				(self,	lowerCamelCase_   ):

       '''simple docstring'''



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

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




      def      a__				(self,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_ = 4,	lowerCamelCase_ = 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   ):
        lowerCamelCase__	:     Any								=		timestep.to(self.timesteps.device   )
       lowerCamelCase__	:     int								=		(self.timesteps == timestep).nonzero().item()
       lowerCamelCase__	:     List[Any]								=		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__	:     str								=		model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
       elif self.config.prediction_type == "sample":
        lowerCamelCase__	:     Any								=		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__	:     str								=		(sample - pred_original_sample) / sigma
       self.derivatives.append(lowerCamelCase_   )
       if len(self.derivatives   ) > order:
        self.derivatives.pop(0   )

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

       # 4. Compute previous sample based on the derivatives path
       lowerCamelCase__	:     int								=		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      a__				(self,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	):

       '''simple docstring'''



       lowerCamelCase__	:     int								=		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
        lowerCamelCase__	:     str								=		self.timesteps.to(original_samples.device,	dtype=torch.floataa   )
        lowerCamelCase__	:     Tuple								=		timesteps.to(original_samples.device,	dtype=torch.floataa   )
       else:
        lowerCamelCase__	:     List[Any]								=		self.timesteps.to(original_samples.device   )
        lowerCamelCase__	:     Optional[int]								=		timesteps.to(original_samples.device   )

       lowerCamelCase__	:     List[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__	:     Dict								=		sigma.unsqueeze(-1   )

       lowerCamelCase__	:     Any								=		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")

