
import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput




def    __UpperCamelCase     (				lowerCAmelCase__							:				List[Any]  ,   lowerCAmelCase__							:				List[Any]=0.9_99  ,   lowerCAmelCase__							:				Tuple="cosine"  ,   ):
 if alpha_transform_type == "cosine":

  def alpha_bar_fn(lowerCAmelCase__							:				int  ):
   return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2  ) ** 2

 elif alpha_transform_type == "exp":

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

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

 __a :  Optional[Any]						=  []
 for i in range(lowerCAmelCase__  ):
  __a :  Tuple						=  i / num_diffusion_timesteps
  __a :  Union[str, Any]						=  (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 		UpperCamelCase__  (       __lowercase    ,__lowercase    ):
   _SCREAMING_SNAKE_CASE      :							int	       =      [e.name for e in KarrasDiffusionSchedulers]
   _SCREAMING_SNAKE_CASE      :							Dict	       =      2
   @register_to_config
   def __init__(self :					List[str]					,				snake_case_ :					int = 1_0_0_0					,				snake_case_ :					float = 0.0_0085					,				snake_case_ :					float = 0.012					,				snake_case_ :					str = "linear"					,				snake_case_ :					Optional[Union[np.ndarray, List[float]]] = None					,				snake_case_ :					str = "epsilon"					,				snake_case_ :					str = "linspace"					,				snake_case_ :					int = 0					,				):
    if trained_betas is not None:
     __a :  Optional[Any]						=  torch.tensor(snake_case_					,				dtype=torch.floataa   )
    elif beta_schedule == "linear":
     __a :  int						=  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.
     __a :  Union[str, Any]						=  (
         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
     __a :  Union[str, Any]						=  betas_for_alpha_bar(snake_case_   )
    else:
     raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}"   )

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

    #  set all values
    self.set_timesteps(snake_case_					,				snake_case_					,				snake_case_   )
   def       lowerCAmelCase			(self :					Optional[Any]					,				snake_case_ :					Optional[Any]					,				snake_case_ :					Dict=None   ):
    if schedule_timesteps is None:
     __a :  List[str]						=  self.timesteps

    __a :  List[str]						=  (schedule_timesteps == timestep).nonzero()

    # The sigma index that is taken for the **very** first `step`
    # is always the second index (or the last index if there is only 1)
    # This way we can ensure we don't accidentally skip a sigma in
    # case we start in the middle of the denoising schedule (e.g. for image-to-image)
    if len(self._index_counter   ) == 0:
     __a :  Optional[Any]						=  1 if len(snake_case_   ) > 1 else 0
    else:
     __a :  List[str]						=  timestep.cpu().item() if torch.is_tensor(snake_case_   ) else timestep
     __a :  Union[str, Any]						=  self._index_counter[timestep_int]

    return indices[pos].item()
   @property
   def       lowerCAmelCase			(self :					List[Any]   ):
    # 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       lowerCAmelCase			(self :					List[Any]					,				snake_case_ :					torch.FloatTensor					,				snake_case_ :					Union[float, torch.FloatTensor]					,				):
    __a :  Any						=  self.index_for_timestep(snake_case_   )

    if self.state_in_first_order:
     __a :  Optional[int]						=  self.sigmas[step_index]
    else:
     __a :  str						=  self.sigmas_interpol[step_index]

    __a :  Tuple						=  sample / ((sigma**2 + 1) ** 0.5)
    return sample
   def       lowerCAmelCase			(self :					Any					,				snake_case_ :					int					,				snake_case_ :					Union[str, torch.device] = None					,				snake_case_ :					Optional[int] = None					,				):
    __a :  Any						=  num_inference_steps

    __a :  Optional[int]						=  num_train_timesteps or self.config.num_train_timesteps

    # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
    if self.config.timestep_spacing == "linspace":
     __a :  Optional[int]						=  np.linspace(0					,				num_train_timesteps - 1					,				snake_case_					,				dtype=snake_case_   )[::-1].copy()
    elif self.config.timestep_spacing == "leading":
     __a :  List[str]						=  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
     __a :  List[str]						=  (np.arange(0					,				snake_case_   ) * step_ratio).round()[::-1].copy().astype(snake_case_   )
     timesteps += self.config.steps_offset
    elif self.config.timestep_spacing == "trailing":
     __a :  Union[str, Any]						=  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
     __a :  int						=  (np.arange(snake_case_					,				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'."   )

    __a :  Dict						=  np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5   )
    __a :  Optional[Any]						=  torch.from_numpy(np.log(snake_case_   )   ).to(snake_case_   )

    __a :  Tuple						=  np.interp(snake_case_					,				np.arange(0					,				len(snake_case_   )   )					,				snake_case_   )
    __a :  int						=  np.concatenate([sigmas, [0.0]]   ).astype(np.floataa   )
    __a :  Optional[int]						=  torch.from_numpy(snake_case_   ).to(device=snake_case_   )

    # interpolate sigmas
    __a :  Optional[int]						=  sigmas.log().lerp(sigmas.roll(1   ).log()					,				0.5   ).exp()

    __a :  List[str]						=  torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2   ), sigmas[-1:]]   )
    __a :  Dict						=  torch.cat(
        [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2   ), sigmas_interpol[-1:]]   )

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

    # interpolate timesteps
    __a :  str						=  self.sigma_to_t(snake_case_   ).to(snake_case_					,				dtype=timesteps.dtype   )
    __a :  Dict						=  torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])					,				dim=-1   ).flatten()

    __a :  int						=  torch.cat([timesteps[:1], interleaved_timesteps]   )

    __a :  List[str]						=  None

    # for exp beta schedules, such as the one for `pipeline_shap_e.py`
    # we need an index counter
    __a :  List[str]						=  defaultdict(snake_case_   )
   def       lowerCAmelCase			(self :					Dict					,				snake_case_ :					Optional[int]   ):
    # get log sigma
    __a :  Any						=  sigma.log()

    # get distribution
    __a :  List[str]						=  log_sigma - self.log_sigmas[:, None]

    # get sigmas range
    __a :  Dict						=  dists.ge(0   ).cumsum(dim=0   ).argmax(dim=0   ).clamp(max=self.log_sigmas.shape[0] - 2   )
    __a :  Optional[Any]						=  low_idx + 1

    __a :  Any						=  self.log_sigmas[low_idx]
    __a :  Optional[int]						=  self.log_sigmas[high_idx]

    # interpolate sigmas
    __a :  Optional[int]						=  (low - log_sigma) / (low - high)
    __a :  str						=  w.clamp(0					,				1   )

    # transform interpolation to time range
    __a :  Dict						=  (1 - w) * low_idx + w * high_idx
    __a :  List[Any]						=  t.view(sigma.shape   )
    return t
   @property
   def       lowerCAmelCase			(self :					Dict   ):
    return self.sample is None
   def       lowerCAmelCase			(self :					Optional[int]					,				snake_case_ :					Union[torch.FloatTensor, np.ndarray]					,				snake_case_ :					Union[float, torch.FloatTensor]					,				snake_case_ :					Union[torch.FloatTensor, np.ndarray]					,				snake_case_ :					bool = True					,				):
    __a :  Optional[int]						=  self.index_for_timestep(snake_case_   )

    # advance index counter by 1
    __a :  List[Any]						=  timestep.cpu().item() if torch.is_tensor(snake_case_   ) else timestep
    self._index_counter[timestep_int] += 1

    if self.state_in_first_order:
     __a :  str						=  self.sigmas[step_index]
     __a :  Optional[Any]						=  self.sigmas_interpol[step_index + 1]
     __a :  Any						=  self.sigmas[step_index + 1]
    else:
     # 2nd order / KDPM2's method
     __a :  List[str]						=  self.sigmas[step_index - 1]
     __a :  List[str]						=  self.sigmas_interpol[step_index]
     __a :  str						=  self.sigmas[step_index]

    # currently only gamma=0 is supported. This usually works best anyways.
    # We can support gamma in the future but then need to scale the timestep before
    # passing it to the model which requires a change in API
    __a :  Optional[Any]						=  0
    __a :  Any						=  sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

    # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
    if self.config.prediction_type == "epsilon":
     __a :  Tuple						=  sigma_hat if self.state_in_first_order else sigma_interpol
     __a :  Dict						=  sample - sigma_input * model_output
    elif self.config.prediction_type == "v_prediction":
     __a :  str						=  sigma_hat if self.state_in_first_order else sigma_interpol
     __a :  List[str]						=  model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
         sample / (sigma_input**2 + 1)
     )
    elif self.config.prediction_type == "sample":
     raise NotImplementedError('''prediction_type not implemented yet: sample'''   )
    else:
     raise ValueError(
         f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"   )

    if self.state_in_first_order:
     # 2. Convert to an ODE derivative for 1st order
     __a :  str						=  (sample - pred_original_sample) / sigma_hat
     # 3. delta timestep
     __a :  int						=  sigma_interpol - sigma_hat

     # store for 2nd order step
     __a :  str						=  sample
    else:
     # DPM-Solver-2
     # 2. Convert to an ODE derivative for 2nd order
     __a :  Dict						=  (sample - pred_original_sample) / sigma_interpol

     # 3. delta timestep
     __a :  Optional[Any]						=  sigma_next - sigma_hat

     __a :  int						=  self.sample
     __a :  str						=  None

    __a :  Tuple						=  sample + derivative * dt

    if not return_dict:
     return (prev_sample,)

    return SchedulerOutput(prev_sample=snake_case_   )
   def       lowerCAmelCase			(self :					List[str]					,				snake_case_ :					torch.FloatTensor					,				snake_case_ :					torch.FloatTensor					,				snake_case_ :					torch.FloatTensor					,				):
    # Make sure sigmas and timesteps have the same device and dtype as original_samples
    __a :  int						=  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
     __a :  str						=  self.timesteps.to(original_samples.device					,				dtype=torch.floataa   )
     __a :  List[str]						=  timesteps.to(original_samples.device					,				dtype=torch.floataa   )
    else:
     __a :  List[Any]						=  self.timesteps.to(original_samples.device   )
     __a :  int						=  timesteps.to(original_samples.device   )

    __a :  List[Any]						=  [self.index_for_timestep(snake_case_					,				snake_case_   ) for t in timesteps]

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

    __a :  Optional[int]						=  original_samples + noise * sigma
    return noisy_samples







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


from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt




def    __UpperCamelCase     (				lowerCAmelCase__							:				int  ):
 __a :  int						=  int(number**0.5  )
 return number == sq * sq




def    __UpperCamelCase     (				lowerCAmelCase__							:				int  ,   lowerCAmelCase__							:				int  ,   lowerCAmelCase__							:				int  ,   lowerCAmelCase__							:				int  ,   lowerCAmelCase__							:				int  ,   lowerCAmelCase__							:				int  ):
 __a :  int						=  x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
 __a :  int						=  x_den * y_den * z_den
 __a :  int						=  gcd(lowerCAmelCase__  ,   lowerCAmelCase__  )
 top //= hcf
 bottom //= hcf
 return top, bottom




def    __UpperCamelCase     (				lowerCAmelCase__							:				int = 3_5  ):
 __a :  set						=  set()
 __a :  int
 __a :  Fraction						=  Fraction(0  )
 __a :  tuple[int, int]

 for x_num in range(1  ,   order + 1  ):
  for x_den in range(x_num + 1  ,   order + 1  ):
   for y_num in range(1  ,   order + 1  ):
    for y_den in range(y_num + 1  ,   order + 1  ):
     # n=1
     __a :  Any						=  x_num * y_den + x_den * y_num
     __a :  Dict						=  x_den * y_den
     __a :  int						=  gcd(lowerCAmelCase__  ,   lowerCAmelCase__  )
     z_num //= hcf
     z_den //= hcf
     if 0 < z_num < z_den <= order:
      __a :  str						=  add_three(
          lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  )
      unique_s.add(lowerCAmelCase__  )

     # n=2
     __a :  Union[str, Any]						=  (
         x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
     )
     __a :  Optional[Any]						=  x_den * x_den * y_den * y_den
     if is_sq(lowerCAmelCase__  ) and is_sq(lowerCAmelCase__  ):
      __a :  Any						=  int(sqrt(lowerCAmelCase__  )  )
      __a :  Optional[Any]						=  int(sqrt(lowerCAmelCase__  )  )
      __a :  int						=  gcd(lowerCAmelCase__  ,   lowerCAmelCase__  )
      z_num //= hcf
      z_den //= hcf
      if 0 < z_num < z_den <= order:
       __a :  str						=  add_three(
           lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  )
       unique_s.add(lowerCAmelCase__  )

                    # n=-1
     __a :  List[str]						=  x_num * y_num
     __a :  List[str]						=  x_den * y_num + x_num * y_den
     __a :  str						=  gcd(lowerCAmelCase__  ,   lowerCAmelCase__  )
     z_num //= hcf
     z_den //= hcf
     if 0 < z_num < z_den <= order:
      __a :  Optional[int]						=  add_three(
          lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  )
      unique_s.add(lowerCAmelCase__  )

     # n=2
     __a :  List[str]						=  x_num * x_num * y_num * y_num
     __a :  Optional[int]						=  (
         x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
     )
     if is_sq(lowerCAmelCase__  ) and is_sq(lowerCAmelCase__  ):
      __a :  Union[str, Any]						=  int(sqrt(lowerCAmelCase__  )  )
      __a :  List[str]						=  int(sqrt(lowerCAmelCase__  )  )
      __a :  Optional[int]						=  gcd(lowerCAmelCase__  ,   lowerCAmelCase__  )
      z_num //= hcf
      z_den //= hcf
      if 0 < z_num < z_den <= order:
       __a :  int						=  add_three(
           lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  )
       unique_s.add(lowerCAmelCase__  )

 for num, den in unique_s:
  total += Fraction(lowerCAmelCase__  ,   lowerCAmelCase__  )

 return total.denominator + total.numerator


if __name__ == "__main__":
      print(F"""{solution() = }""")
