'''simple docstring'''


# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin, SchedulerOutput





@dataclass
class       _a    (		__a      ):


  """simple docstring"""

  A_    							=						42
  A_    							=						42






class       _a    (		__a ,				__a      ):


  """simple docstring"""

  A_    							=						1




  @register_to_config
  def __init__(		self      :       Dict   ,				lowercase_      :       int = 2_000   ,				lowercase_      :       float = 0.1_5   ,				lowercase_      :       float = 0.0_1   ,				lowercase_      :       float = 1_3_4_8.0   ,				lowercase_      :       float = 1e-5   ,				lowercase_      :       int = 1   ,				):







    '''simple docstring'''


    lowercase_     =       sigma_max

    # setable values
    lowercase_     =       None

    self.set_sigmas(lowercase_   ,				lowercase_   ,				lowercase_   ,				lowercase_      )




  def 		lowerCamelCase__  (		self      :       Dict   ,				lowercase_      :       torch.FloatTensor   ,				lowercase_      :       Optional[int] = None      ):







    '''simple docstring'''


    return sample




  def 		lowerCamelCase__  (		self      :       Optional[int]   ,				lowercase_      :       int   ,				lowercase_      :       float = None   ,				lowercase_      :       Union[str, torch.device] = None      ):







    '''simple docstring'''


    lowercase_     =       sampling_eps if sampling_eps is not None else self.config.sampling_eps

    lowercase_     =       torch.linspace(1   ,				lowercase_   ,				lowercase_   ,				device=lowercase_      )




  def 		lowerCamelCase__  (		self      :       int   ,				lowercase_      :       int   ,				lowercase_      :       float = None   ,				lowercase_      :       float = None   ,				lowercase_      :       float = None      ):







    '''simple docstring'''


    lowercase_     =       sigma_min if sigma_min is not None else self.config.sigma_min
    lowercase_     =       sigma_max if sigma_max is not None else self.config.sigma_max
    lowercase_     =       sampling_eps if sampling_eps is not None else self.config.sampling_eps
    if self.timesteps is None:
      self.set_timesteps(lowercase_   ,				lowercase_      )

    lowercase_     =       sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
    lowercase_     =       torch.exp(torch.linspace(math.log(lowercase_      )   ,				math.log(lowercase_      )   ,				lowercase_      )      )
    lowercase_     =       torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]      )




  def 		lowerCamelCase__  (		self      :       Any   ,				lowercase_      :       Tuple   ,				lowercase_      :       Union[str, Any]      ):







    '''simple docstring'''


    return torch.where(
        timesteps == 0   ,				torch.zeros_like(t.to(timesteps.device      )      )   ,				self.discrete_sigmas[timesteps - 1].to(timesteps.device      )   ,				)




  def 		lowerCamelCase__  (		self      :       List[str]   ,				lowercase_      :       torch.FloatTensor   ,				lowercase_      :       int   ,				lowercase_      :       torch.FloatTensor   ,				lowercase_      :       Optional[torch.Generator] = None   ,				lowercase_      :       bool = True   ,				):







    '''simple docstring'''


    if self.timesteps is None:
      raise ValueError(
          """`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""      )

    lowercase_     =       timestep * torch.ones(
        sample.shape[0]   ,				device=sample.device      )  # torch.repeat_interleave(timestep, sample.shape[0])
    lowercase_     =       (timestep * (len(self.timesteps      ) - 1)).long()

    # mps requires indices to be in the same device, so we use cpu as is the default with cuda
    lowercase_     =       timesteps.to(self.discrete_sigmas.device      )

    lowercase_     =       self.discrete_sigmas[timesteps].to(sample.device      )
    lowercase_     =       self.get_adjacent_sigma(lowercase_   ,				lowercase_      ).to(sample.device      )
    lowercase_     =       torch.zeros_like(lowercase_      )
    lowercase_     =       (sigma**2 - adjacent_sigma**2) ** 0.5

    # equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
    # also equation 47 shows the analog from SDE models to ancestral sampling methods
    lowercase_     =       diffusion.flatten()
    while len(diffusion.shape      ) < len(sample.shape      ):
      lowercase_     =       diffusion.unsqueeze(-1      )
    lowercase_     =       drift - diffusion**2 * model_output

    #  equation 6: sample noise for the diffusion term of
    lowercase_     =       randn_tensor(
        sample.shape   ,				layout=sample.layout   ,				generator=lowercase_   ,				device=sample.device   ,				dtype=sample.dtype      )
    lowercase_     =       sample - drift  # subtract because `dt` is a small negative timestep
    # TODO is the variable diffusion the correct scaling term for the noise?
    lowercase_     =       prev_sample_mean + diffusion * noise  # add impact of diffusion field g

    if not return_dict:
      return (prev_sample, prev_sample_mean)

    return SdeVeOutput(prev_sample=lowercase_   ,				prev_sample_mean=lowercase_      )




  def 		lowerCamelCase__  (		self      :       Dict   ,				lowercase_      :       torch.FloatTensor   ,				lowercase_      :       torch.FloatTensor   ,				lowercase_      :       Optional[torch.Generator] = None   ,				lowercase_      :       bool = True   ,				):







    '''simple docstring'''


    if self.timesteps is None:
      raise ValueError(
          """`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""      )

    # For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
    # sample noise for correction
    lowercase_     =       randn_tensor(sample.shape   ,				layout=sample.layout   ,				generator=lowercase_      ).to(sample.device      )

    # compute step size from the model_output, the noise, and the snr
    lowercase_     =       torch.norm(model_output.reshape(model_output.shape[0]   ,				-1      )   ,				dim=-1      ).mean()
    lowercase_     =       torch.norm(noise.reshape(noise.shape[0]   ,				-1      )   ,				dim=-1      ).mean()
    lowercase_     =       (self.config.snr * noise_norm / grad_norm) ** 2 * 2
    lowercase_     =       step_size * torch.ones(sample.shape[0]      ).to(sample.device      )
    # self.repeat_scalar(step_size, sample.shape[0])

    # compute corrected sample: model_output term and noise term
    lowercase_     =       step_size.flatten()
    while len(step_size.shape      ) < len(sample.shape      ):
      lowercase_     =       step_size.unsqueeze(-1      )
    lowercase_     =       sample + step_size * model_output
    lowercase_     =       prev_sample_mean + ((step_size * 2) ** 0.5) * noise

    if not return_dict:
      return (prev_sample,)

    return SchedulerOutput(prev_sample=lowercase_      )




  def 		lowerCamelCase__  (		self      :       Tuple   ,				lowercase_      :       torch.FloatTensor   ,				lowercase_      :       torch.FloatTensor   ,				lowercase_      :       torch.FloatTensor   ,				):







    '''simple docstring'''


    lowercase_     =       timesteps.to(original_samples.device      )
    lowercase_     =       self.discrete_sigmas.to(original_samples.device      )[timesteps]
    lowercase_     =       (
        noise * sigmas[:, None, None, None]
        if noise is not None
        else torch.randn_like(lowercase_      ) * sigmas[:, None, None, None]
    )
    lowercase_     =       noise + original_samples
    return noisy_samples





  def __len__(		self      :       Union[str, Any]      ):







    '''simple docstring'''


    return self.config.num_train_timesteps


'''simple docstring'''


import math
import sys

def   A_      (       SCREAMING_SNAKE_CASE_						)			->int:
  if number != int(SCREAMING_SNAKE_CASE_						):
    raise ValueError("""the value of input must be a natural number"""						)
  if number < 0:
    raise ValueError("""the value of input must not be a negative number"""						)
  if number == 0:
    return 1
  lowercase_     =       [-1] * (number + 1)
  lowercase_     =       0
  for i in range(1 ,	number + 1						):
    lowercase_     =       sys.maxsize
    lowercase_     =       int(math.sqrt(SCREAMING_SNAKE_CASE_						)						)
    for j in range(1 ,	root + 1						):
      lowercase_     =       1 + answers[i - (j**2)]
      lowercase_     =       min(SCREAMING_SNAKE_CASE_ ,	SCREAMING_SNAKE_CASE_						)
    lowercase_     =       answer
  return answers[number]


if __name__ == "__main__":
       import doctest

       doctest.testmod()

