


'''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 							UpperCAmelCase ( _snake_case	):
 UpperCAmelCase				=				42
 UpperCAmelCase				=				None


def 					a__    (				UpperCamelCase_	:			Any,      UpperCamelCase_	:			int=0.999,      UpperCamelCase_	:			Tuple="cosine",      ):
   if alpha_transform_type == "cosine":

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

   elif alpha_transform_type == "exp":

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

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

   UpperCAmelCase__  :Any            =			[]
   for i in range(UpperCamelCase_	):
      UpperCAmelCase__  :Union[str, Any]            =			i / num_diffusion_timesteps
      UpperCAmelCase__  :List[Any]            =			(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 							UpperCAmelCase ( _snake_case	,   _snake_case	):
 UpperCAmelCase				=				[e.name for e in KarrasDiffusionSchedulers]
 UpperCAmelCase				=				1


 @register_to_config
 def __init__(			self       :  Optional[int] ,					__lowerCamelCase       :  int = 1_0_0_0 ,					__lowerCamelCase       :  float = 0.00_01 ,					__lowerCamelCase       :  float = 0.02 ,					__lowerCamelCase       :  str = "linear" ,					__lowerCamelCase       :  Optional[Union[np.ndarray, List[float]]] = None ,					__lowerCamelCase       :  Optional[bool] = False ,					__lowerCamelCase       :  str = "epsilon" ,					__lowerCamelCase       :  str = "linspace" ,					__lowerCamelCase       :  int = 0 ,					):
    if trained_betas is not None:
       UpperCAmelCase__  :Dict            =			torch.tensor(__lowerCamelCase ,					dtype=torch.floataa   )
    elif beta_schedule == "linear":
       UpperCAmelCase__  :List[Any]            =			torch.linspace(__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase ,					dtype=torch.floataa   )
    elif beta_schedule == "scaled_linear":
       # this schedule is very specific to the latent diffusion model.
       UpperCAmelCase__  :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
       UpperCAmelCase__  :Union[str, Any]            =			betas_for_alpha_bar(__lowerCamelCase   )
    else:
       raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''   )

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

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

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


 @property
 def 					__SCREAMING_SNAKE_CASE				(			self       :  Dict   ):
    # 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 					__SCREAMING_SNAKE_CASE				(			self       :  str ,					__lowerCamelCase       :  torch.FloatTensor ,					__lowerCamelCase       :  Union[float, torch.FloatTensor]   ):
    if isinstance(__lowerCamelCase ,					torch.Tensor   ):
       UpperCAmelCase__  :Any            =			timestep.to(self.timesteps.device   )
    UpperCAmelCase__  :Tuple            =			(self.timesteps == timestep).nonzero().item()
    UpperCAmelCase__  :str            =			self.sigmas[step_index]
    UpperCAmelCase__  :Union[str, Any]            =			sample / ((sigma**2 + 1) ** 0.5)
    UpperCAmelCase__  :str            =			True
    return sample


 def 					__SCREAMING_SNAKE_CASE				(			self       :  Any ,					__lowerCamelCase       :  Union[str, Any] ,					__lowerCamelCase       :  Tuple ,					__lowerCamelCase       :  Tuple   ):

    def lms_derivative(__lowerCamelCase       :  Optional[Any]   ):
       UpperCAmelCase__  :Tuple            =			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__  :int            =			integrate.quad(__lowerCamelCase ,					self.sigmas[t] ,					self.sigmas[t + 1] ,					epsrel=1e-4   )[0]

    return integrated_coeff


 def 					__SCREAMING_SNAKE_CASE				(			self       :  Optional[Any] ,					__lowerCamelCase       :  int ,					__lowerCamelCase       :  Union[str, torch.device] = None   ):
    UpperCAmelCase__  :List[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":
       UpperCAmelCase__  :List[Any]            =			np.linspace(0 ,					self.config.num_train_timesteps - 1 ,					__lowerCamelCase ,					dtype=__lowerCamelCase   )[
           ::-1
       ].copy()
    elif self.config.timestep_spacing == "leading":
       UpperCAmelCase__  :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
       UpperCAmelCase__  :Optional[int]            =			(np.arange(0 ,					__lowerCamelCase   ) * step_ratio).round()[::-1].copy().astype(__lowerCamelCase   )
       timesteps += self.config.steps_offset
    elif self.config.timestep_spacing == "trailing":
       UpperCAmelCase__  :int            =			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__  :Any            =			(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__  :Optional[Any]            =			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5   )
    UpperCAmelCase__  :Tuple            =			np.log(__lowerCamelCase   )
    UpperCAmelCase__  :Tuple            =			np.interp(__lowerCamelCase ,					np.arange(0 ,					len(__lowerCamelCase   )   ) ,					__lowerCamelCase   )

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

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

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

    UpperCAmelCase__  :Union[str, Any]            =			[]


 def 					__SCREAMING_SNAKE_CASE				(			self       :  int ,					__lowerCamelCase       :  Union[str, Any] ,					__lowerCamelCase       :  Union[str, Any]   ):
    # get log sigma
    UpperCAmelCase__  :Optional[Any]            =			np.log(__lowerCamelCase   )

    # get distribution
    UpperCAmelCase__  :List[Any]            =			log_sigma - log_sigmas[:, np.newaxis]

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

    UpperCAmelCase__  :str            =			log_sigmas[low_idx]
    UpperCAmelCase__  :Union[str, Any]            =			log_sigmas[high_idx]

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

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


 def 					__SCREAMING_SNAKE_CASE				(			self       :  Union[str, Any] ,					__lowerCamelCase       :  torch.FloatTensor   ):
    UpperCAmelCase__  :float            =			in_sigmas[-1].item()
    UpperCAmelCase__  :float            =			in_sigmas[0].item()

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


 def 					__SCREAMING_SNAKE_CASE				(			self       :  List[Any] ,					__lowerCamelCase       :  torch.FloatTensor ,					__lowerCamelCase       :  Union[float, torch.FloatTensor] ,					__lowerCamelCase       :  torch.FloatTensor ,					__lowerCamelCase       :  int = 4 ,					__lowerCamelCase       :  bool = 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(__lowerCamelCase ,					torch.Tensor   ):
       UpperCAmelCase__  :Dict            =			timestep.to(self.timesteps.device   )
    UpperCAmelCase__  :Optional[int]            =			(self.timesteps == timestep).nonzero().item()
    UpperCAmelCase__  :Any            =			self.sigmas[step_index]

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

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

    # 4. Compute previous sample based on the derivatives path
    UpperCAmelCase__  :Tuple            =			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 					__SCREAMING_SNAKE_CASE				(			self       :  Optional[int] ,					__lowerCamelCase       :  torch.FloatTensor ,					__lowerCamelCase       :  torch.FloatTensor ,					__lowerCamelCase       :  torch.FloatTensor ,					):
    # Make sure sigmas and timesteps have the same device and dtype as original_samples
    UpperCAmelCase__  :Tuple            =			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__  :List[str]            =			self.timesteps.to(original_samples.device ,					dtype=torch.floataa   )
       UpperCAmelCase__  :List[str]            =			timesteps.to(original_samples.device ,					dtype=torch.floataa   )
    else:
       UpperCAmelCase__  :Optional[int]            =			self.timesteps.to(original_samples.device   )
       UpperCAmelCase__  :List[str]            =			timesteps.to(original_samples.device   )

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

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

    UpperCAmelCase__  :List[str]            =			original_samples + noise * sigma
    return noisy_samples





 def __len__(			self       :  Optional[Any]   ):
    return self.config.num_train_timesteps







'''simple docstring'''





def 					a__    (				UpperCamelCase_	:			int	):
   UpperCAmelCase__  :str            =			[True for i in range(n + 1	)]
   UpperCAmelCase__  :List[str]            =			[i - 1 for i in range(n + 1	)]
   UpperCAmelCase__  :str            =			[]
   for i in range(2,      n + 1	):
      if is_prime[i]:
         primes.append(UpperCamelCase_	)
      for j in range(0,      len(UpperCamelCase_	)	):
         if i * primes[j] >= n:
            break
         UpperCAmelCase__  :List[str]            =			False

         if i % primes[j] == 0:
            UpperCAmelCase__  :Any            =			totients[i] * primes[j]
            break

         UpperCAmelCase__  :str            =			totients[i] * (primes[j] - 1)

   return totients


if __name__ == "__main__":
    import doctest

    doctest.testmod()



