




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_       (      __UpperCamelCase,							__UpperCamelCase=0.999,							__UpperCamelCase="cosine",							):
    if alpha_transform_type == "cosine":

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

    elif alpha_transform_type == "exp":

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

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

    SCREAMING_SNAKE_CASE__        =[]
    for i in range(__UpperCamelCase      ):
        SCREAMING_SNAKE_CASE__        =i / num_diffusion_timesteps
        SCREAMING_SNAKE_CASE__        =(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  __a   (					__lowerCamelCase				,	__lowerCamelCase	):


     """simple docstring"""


     _A							:       List[str]							   =    [e.name for e in KarrasDiffusionSchedulers]
     _A							:       Dict							   =    2




     @register_to_config
     def __init__(      self     :					List[str]							,_UpperCamelCase     :					List[Any] = 1_0_0_0							,_UpperCamelCase     :					Tuple = 0.0_0085							,_UpperCamelCase     :					Any = 0.012							,_UpperCamelCase     :					str = "linear"							,_UpperCamelCase     :					int = None							,_UpperCamelCase     :					Optional[Any] = "epsilon"							,_UpperCamelCase     :					int = "linspace"							,_UpperCamelCase     :					str = 0							,)						->  Tuple:


         '''simple docstring'''





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

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

         #  set all values
         self.set_timesteps(a_							,a_							,a_		)




     def     __A							(      self     :					Any							,_UpperCamelCase     :					str							,_UpperCamelCase     :					Dict=None		)						->  Optional[Any]:


         '''simple docstring'''





         if schedule_timesteps is None:
             SCREAMING_SNAKE_CASE__        =self.timesteps

         SCREAMING_SNAKE_CASE__        =(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:
             SCREAMING_SNAKE_CASE__        =1 if len(a_		) > 1 else 0
         else:
             SCREAMING_SNAKE_CASE__        =timestep.cpu().item() if torch.is_tensor(a_		) else timestep
             SCREAMING_SNAKE_CASE__        =self._index_counter[timestep_int]

         return indices[pos].item()




     @property
     def     __A							(      self     :					List[Any]		)						->  Union[str, Any]:


         '''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     :					List[Any]							,_UpperCamelCase     :					Dict							,_UpperCamelCase     :					Any							,)						->  torch.FloatTensor:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__        =self.index_for_timestep(a_		)

         if self.state_in_first_order:
             SCREAMING_SNAKE_CASE__        =self.sigmas[step_index]
         else:
             SCREAMING_SNAKE_CASE__        =self.sigmas_interpol[step_index]

         SCREAMING_SNAKE_CASE__        =sample / ((sigma**2 + 1) ** 0.5)
         return sample




     def     __A							(      self     :					List[str]							,_UpperCamelCase     :					Dict							,_UpperCamelCase     :					int = None							,_UpperCamelCase     :					Dict = None							,)						->  Dict:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__        =num_inference_steps

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

         SCREAMING_SNAKE_CASE__        =np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5		)
         SCREAMING_SNAKE_CASE__        =torch.from_numpy(np.log(a_		)		).to(a_		)

         SCREAMING_SNAKE_CASE__        =np.interp(a_							,np.arange(0							,len(a_		)		)							,a_		)
         SCREAMING_SNAKE_CASE__        =np.concatenate([sigmas, [0.0]]		).astype(np.floataa		)
         SCREAMING_SNAKE_CASE__        =torch.from_numpy(a_		).to(device=a_		)

         # interpolate sigmas
         SCREAMING_SNAKE_CASE__        =sigmas.log().lerp(sigmas.roll(1		).log()							,0.5		).exp()

         SCREAMING_SNAKE_CASE__        =torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2		), sigmas[-1:]]		)
         SCREAMING_SNAKE_CASE__        =torch.cat(
             [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2		), sigmas_interpol[-1:]]		)

         if str(a_		).startswith("""mps"""		):
             # mps does not support float64
             SCREAMING_SNAKE_CASE__        =torch.from_numpy(a_		).to(a_							,dtype=torch.floataa		)
         else:
             SCREAMING_SNAKE_CASE__        =torch.from_numpy(a_		).to(a_		)

         # interpolate timesteps
         SCREAMING_SNAKE_CASE__        =self.sigma_to_t(a_		).to(a_							,dtype=timesteps.dtype		)
         SCREAMING_SNAKE_CASE__        =torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])							,dim=-1		).flatten()

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

         SCREAMING_SNAKE_CASE__        =None

         # for exp beta schedules, such as the one for `pipeline_shap_e.py`
         # we need an index counter
         SCREAMING_SNAKE_CASE__        =defaultdict(a_		)




     def     __A							(      self     :					Optional[int]							,_UpperCamelCase     :					Tuple		)						->  Tuple:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__        =sigma.log()

         # get distribution
         SCREAMING_SNAKE_CASE__        =log_sigma - self.log_sigmas[:, None]

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

         SCREAMING_SNAKE_CASE__        =self.log_sigmas[low_idx]
         SCREAMING_SNAKE_CASE__        =self.log_sigmas[high_idx]

         # interpolate sigmas
         SCREAMING_SNAKE_CASE__        =(low - log_sigma) / (low - high)
         SCREAMING_SNAKE_CASE__        =w.clamp(0							,1		)

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




     @property
     def     __A							(      self     :					Dict		)						->  Optional[Any]:


         '''simple docstring'''





         return self.sample is None




     def     __A							(      self     :					Dict							,_UpperCamelCase     :					int							,_UpperCamelCase     :					Tuple							,_UpperCamelCase     :					List[str]							,_UpperCamelCase     :					int = True							,)						->  Union[SchedulerOutput, Tuple]:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__        =self.index_for_timestep(a_		)

         # advance index counter by 1
         SCREAMING_SNAKE_CASE__        =timestep.cpu().item() if torch.is_tensor(a_		) else timestep
         self._index_counter[timestep_int] += 1

         if self.state_in_first_order:
             SCREAMING_SNAKE_CASE__        =self.sigmas[step_index]
             SCREAMING_SNAKE_CASE__        =self.sigmas_interpol[step_index + 1]
             SCREAMING_SNAKE_CASE__        =self.sigmas[step_index + 1]
         else:
             # 2nd order / KDPM2's method
             SCREAMING_SNAKE_CASE__        =self.sigmas[step_index - 1]
             SCREAMING_SNAKE_CASE__        =self.sigmas_interpol[step_index]
             SCREAMING_SNAKE_CASE__        =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
         SCREAMING_SNAKE_CASE__        =0
         SCREAMING_SNAKE_CASE__        =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":
             SCREAMING_SNAKE_CASE__        =sigma_hat if self.state_in_first_order else sigma_interpol
             SCREAMING_SNAKE_CASE__        =sample - sigma_input * model_output
         elif self.config.prediction_type == "v_prediction":
             SCREAMING_SNAKE_CASE__        =sigma_hat if self.state_in_first_order else sigma_interpol
             SCREAMING_SNAKE_CASE__        =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
             SCREAMING_SNAKE_CASE__        =(sample - pred_original_sample) / sigma_hat
             # 3. delta timestep
             SCREAMING_SNAKE_CASE__        =sigma_interpol - sigma_hat

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

             # 3. delta timestep
             SCREAMING_SNAKE_CASE__        =sigma_next - sigma_hat

             SCREAMING_SNAKE_CASE__        =self.sample
             SCREAMING_SNAKE_CASE__        =None

         SCREAMING_SNAKE_CASE__        =sample + derivative * dt

         if not return_dict:
             return (prev_sample,)

         return SchedulerOutput(prev_sample=a_		)




     def     __A							(      self     :					Tuple							,_UpperCamelCase     :					Optional[int]							,_UpperCamelCase     :					Optional[Any]							,_UpperCamelCase     :					Any							,)						->  torch.FloatTensor:


         '''simple docstring'''





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

         SCREAMING_SNAKE_CASE__        =[self.index_for_timestep(a_							,a_		) for t in timesteps]

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

         SCREAMING_SNAKE_CASE__        =original_samples + noise * sigma
         return noisy_samples




     def __len__(      self     :					Dict		)						->  Dict:


         '''simple docstring'''





         return self.config.num_train_timesteps









'''simple docstring'''




def    lowerCamelCase__		(    SCREAMING_SNAKE_CASE   : int = 1000    ):
  UpperCAmelCase    				=						-1
  UpperCAmelCase    				=						0
  for a in range(1							, n // 3    ):
    # Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
    UpperCAmelCase    				=						(n * n - 2 * a * n) // (2 * n - 2 * a)
    UpperCAmelCase    				=						n - a - b
    if c * c == (a * a + b * b):
      UpperCAmelCase    				=						a * b * c
      if candidate >= product:
        UpperCAmelCase    				=						candidate
  return product


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


