




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	(						_lowerCAmelCase						):
     """simple docstring"""

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

def 	lowerCAmelCase_	(     lowerCamelCase:				Optional[int]   , lowerCamelCase:				Any=0.999   , lowerCamelCase:				Any="cosine"   , )    ->	List[str]:


      '''simple docstring'''




      if alpha_transform_type == "cosine":

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

      elif alpha_transform_type == "exp":

            def alpha_bar_fn(lowerCamelCase:				List[str]  ):
                  return math.exp(t * -12.0  )

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

      lowerCamelCase__					     = []
      for i in range(lowerCamelCase  ):
            lowerCamelCase__					     = i / num_diffusion_timesteps
            lowerCamelCase__					     = (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	(						_lowerCAmelCase	,  _lowerCAmelCase						):
     """simple docstring"""

     _snake_case:		Optional[Any]   =[e.name for e in KarrasDiffusionSchedulers]
     _snake_case:		Any   =1




     @register_to_config
     def __init__(			self     :      int		,     A__     :      int = 1_0_0_0		,     A__     :      float = 0.0001		,     A__     :      float = 0.02		,     A__     :      str = "linear"		,     A__     :      Optional[Union[np.ndarray, List[float]]] = None		,     A__     :      Optional[bool] = False		,     A__     :      str = "epsilon"		,     A__     :      str = "linspace"		,     A__     :      int = 0		,     ) ->				Optional[Any]:
           if trained_betas is not None:
                 lowerCamelCase__					     = torch.tensor(A__		,     dtype=torch.floataa	)
           elif beta_schedule == "linear":
                 lowerCamelCase__					     = torch.linspace(A__		,     A__		,     A__		,     dtype=torch.floataa	)
           elif beta_schedule == "scaled_linear":
                 # this schedule is very specific to the latent diffusion model.
                 lowerCamelCase__					     = (
                     torch.linspace(beta_start**0.5		,     beta_end**0.5		,     A__		,     dtype=torch.floataa	) ** 2
                 )
           elif beta_schedule == "squaredcos_cap_v2":
                 # Glide cosine schedule
                 lowerCamelCase__					     = betas_for_alpha_bar(A__	)
           else:
                 raise NotImplementedError(F"""{beta_schedule} does is not implemented for {self.__class__}"""	)

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

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

           # setable values
           lowerCamelCase__					     = None
           lowerCamelCase__					     = use_karras_sigmas
           self.set_timesteps(A__		,     A__	)
           lowerCamelCase__					     = []
           lowerCamelCase__					     = False




     @property
     def        __snake_case      (			self     :      Tuple	) ->				int:
           # 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        __snake_case      (			self     :      str		,     A__     :      torch.FloatTensor		,     A__     :      Union[float, torch.FloatTensor]	) ->				torch.FloatTensor:
           if isinstance(A__		,     torch.Tensor	):
                 lowerCamelCase__					     = timestep.to(self.timesteps.device	)
           lowerCamelCase__					     = (self.timesteps == timestep).nonzero().item()
           lowerCamelCase__					     = self.sigmas[step_index]
           lowerCamelCase__					     = sample / ((sigma**2 + 1) ** 0.5)
           lowerCamelCase__					     = True
           return sample




     def        __snake_case      (			self     :      List[Any]		,     A__     :      List[Any]		,     A__     :      Any		,     A__     :      str	) ->				List[str]:

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

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

           return integrated_coeff




     def        __snake_case      (			self     :      Dict		,     A__     :      int		,     A__     :      Union[str, torch.device] = None	) ->				int:
           lowerCamelCase__					     = 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__					     = np.linspace(0		,     self.config.num_train_timesteps - 1		,     A__		,     dtype=A__	)[
                     ::-1
                 ].copy()
           elif self.config.timestep_spacing == "leading":
                 lowerCamelCase__					     = 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__					     = (np.arange(0		,     A__	) * step_ratio).round()[::-1].copy().astype(A__	)
                 timesteps += self.config.steps_offset
           elif self.config.timestep_spacing == "trailing":
                 lowerCamelCase__					     = 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__					     = (np.arange(self.config.num_train_timesteps		,     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'."""	)

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

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

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

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

           lowerCamelCase__					     = []




     def        __snake_case      (			self     :      List[str]		,     A__     :      Union[str, Any]		,     A__     :      str	) ->				int:
           # get log sigma
           lowerCamelCase__					     = np.log(A__	)

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

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

           lowerCamelCase__					     = log_sigmas[low_idx]
           lowerCamelCase__					     = log_sigmas[high_idx]

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

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




     def        __snake_case      (			self     :      Tuple		,     A__     :      torch.FloatTensor	) ->				torch.FloatTensor:
           lowerCamelCase__					     = in_sigmas[-1].item()
           lowerCamelCase__					     = in_sigmas[0].item()

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




     def        __snake_case      (			self     :      Union[str, Any]		,     A__     :      torch.FloatTensor		,     A__     :      Union[float, torch.FloatTensor]		,     A__     :      torch.FloatTensor		,     A__     :      int = 4		,     A__     :      bool = True		,     ) ->				Union[LMSDiscreteSchedulerOutput, Tuple]:
           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(A__		,     torch.Tensor	):
                 lowerCamelCase__					     = timestep.to(self.timesteps.device	)
           lowerCamelCase__					     = (self.timesteps == timestep).nonzero().item()
           lowerCamelCase__					     = self.sigmas[step_index]

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

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

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

           if not return_dict:
                 return (prev_sample,)

           return LMSDiscreteSchedulerOutput(prev_sample=A__		,     pred_original_sample=A__	)




     def        __snake_case      (			self     :      Tuple		,     A__     :      torch.FloatTensor		,     A__     :      torch.FloatTensor		,     A__     :      torch.FloatTensor		,     ) ->				torch.FloatTensor:
           # Make sure sigmas and timesteps have the same device and dtype as original_samples
           lowerCamelCase__					     = 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
                 lowerCamelCase__					     = self.timesteps.to(original_samples.device		,     dtype=torch.floataa	)
                 lowerCamelCase__					     = timesteps.to(original_samples.device		,     dtype=torch.floataa	)
           else:
                 lowerCamelCase__					     = self.timesteps.to(original_samples.device	)
                 lowerCamelCase__					     = timesteps.to(original_samples.device	)

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

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

           lowerCamelCase__					     = original_samples + noise * sigma
           return noisy_samples




     def __len__(			self     :      List[str]	) ->				Any:
           return self.config.num_train_timesteps





def 	lowerCAmelCase_	(     lowerCamelCase:				int  )    ->	int:


      '''simple docstring'''




      return n * (2 * n - 1)

def 	lowerCAmelCase_	(     lowerCamelCase:				int  )    ->	bool:


      '''simple docstring'''




      lowerCamelCase__					     = (1 + 24 * n) ** 0.5
      return ((1 + root) / 6) % 1 == 0

def 	lowerCAmelCase_	(     lowerCamelCase:				int = 1_44  )    ->	int:


      '''simple docstring'''




      lowerCamelCase__					     = start
      lowerCamelCase__					     = hexagonal_num(lowerCamelCase  )
      while not is_pentagonal(lowerCamelCase  ):
            n += 1
            lowerCamelCase__					     = hexagonal_num(lowerCamelCase  )
      return num


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