




'''simple docstring'''





from functools import lru_cache





@lru_cache
def UpperCAmelCase						(					UpperCAmelCase_	):
    if not isinstance(UpperCAmelCase_      ,  UpperCAmelCase_	):
        raise TypeError("""k must be an integer."""	)
    if k < 0:
        raise ValueError("""k integer must be greater or equal to zero."""	)
    if k == 0:
        return 0
    elif k == 1:
        return 1
    else:
        return fibonacci(k - 1	) + fibonacci(k - 2	)





def UpperCAmelCase						(					UpperCAmelCase_      ,  UpperCAmelCase_	):
    _a							:       Any       					=			len(UpperCAmelCase_	)
    # Find m such that F_m >= n where F_i is the i_th fibonacci number.
    _a							:       Union[str, Any]       					=			0
    while True:
        if fibonacci(UpperCAmelCase_	) >= len_list:
            _a							:       int       					=			i
            break
        i += 1
    _a							:       List[Any]       					=			0
    while fibb_k > 0:
        _a							:       Optional[Any]       					=			min(
            offset + fibonacci(fibb_k - 1	)      ,  len_list - 1	)  # Prevent out of range
        _a							:       str       					=			arr[index_k]
        if item_k_1 == val:
            return index_k
        elif val < item_k_1:
            fibb_k -= 1
        elif val > item_k_1:
            offset += fibonacci(fibb_k - 1	)
            fibb_k -= 2
    else:
        return -1


if __name__ == "__main__":
  import doctest

  doctest.testmod()








'''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__					):
  a    :torch.FloatTensor
  a    :Optional[torch.FloatTensor]      					=				None






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}'''	)

    _a							:       Union[str, Any]       					=			[]
    for i in range(UpperCAmelCase_	):
        _a							:       Optional[int]       					=			i / num_diffusion_timesteps
        _a							:       Optional[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__					):
  a    :Any      					=				[e.name for e in KarrasDiffusionSchedulers]
  a    :Tuple      					=				1



  @register_to_config
  def __init__( self		,    __lowerCAmelCase = 1000		,    __lowerCAmelCase = 0.0001		,    __lowerCAmelCase = 0.02		,    __lowerCAmelCase = "linear"		,    __lowerCAmelCase = None		,    __lowerCAmelCase = False		,    __lowerCAmelCase = "epsilon"		,    __lowerCAmelCase = "linspace"		,    __lowerCAmelCase = 0		,    ):







      '''simple docstring'''


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

      _a							:       Dict       					=			1.0 - self.betas
      _a							:       Any       					=			torch.cumprod(self.alphas		,    dim=0   )

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

      # setable values
      _a							:       Tuple       					=			None
      _a							:       List[Any]       					=			use_karras_sigmas
      self.set_timesteps(__lowerCAmelCase		,    __lowerCAmelCase   )
      _a							:       Dict       					=			[]
      _a							:       int       					=			False



  @property
  def 						a_       ( self   ):







      '''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		,    __lowerCAmelCase		,    __lowerCAmelCase   ):







      '''simple docstring'''


      if isinstance(__lowerCAmelCase		,    torch.Tensor   ):
          _a							:       int       					=			timestep.to(self.timesteps.device   )
      _a							:       Optional[Any]       					=			(self.timesteps == timestep).nonzero().item()
      _a							:       int       					=			self.sigmas[step_index]
      _a							:       Optional[int]       					=			sample / ((sigma**2 + 1) ** 0.5)
      _a							:       str       					=			True
      return sample



  def 						a_       ( self		,    __lowerCAmelCase		,    __lowerCAmelCase		,    __lowerCAmelCase   ):







      '''simple docstring'''


      def lms_derivative(__lowerCAmelCase   ):
          _a							:       Optional[Any]       					=			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

      _a							:       Union[str, Any]       					=			integrate.quad(__lowerCAmelCase		,    self.sigmas[t]		,    self.sigmas[t + 1]		,    epsrel=1e-4   )[0]

      return integrated_coeff



  def 						a_       ( self		,    __lowerCAmelCase		,    __lowerCAmelCase = None   ):







      '''simple docstring'''


      _a							:       Optional[int]       					=			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":
          _a							:       str       					=			np.linspace(0		,    self.config.num_train_timesteps - 1		,    __lowerCAmelCase		,    dtype=__lowerCAmelCase   )[
              ::-1
          ].copy()
      elif self.config.timestep_spacing == "leading":
          _a							:       str       					=			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
          _a							:       List[str]       					=			(np.arange(0		,    __lowerCAmelCase   ) * step_ratio).round()[::-1].copy().astype(__lowerCAmelCase   )
          timesteps += self.config.steps_offset
      elif self.config.timestep_spacing == "trailing":
          _a							:       Optional[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
          _a							:       List[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\'.'''   )

      _a							:       Optional[int]       					=			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5   )
      _a							:       Optional[int]       					=			np.log(__lowerCAmelCase   )
      _a							:       Any       					=			np.interp(__lowerCAmelCase		,    np.arange(0		,    len(__lowerCAmelCase   )   )		,    __lowerCAmelCase   )

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

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

      _a							:       int       					=			torch.from_numpy(__lowerCAmelCase   ).to(device=__lowerCAmelCase   )
      if str(__lowerCAmelCase   ).startswith("""mps"""   ):
          # mps does not support float64
          _a							:       List[str]       					=			torch.from_numpy(__lowerCAmelCase   ).to(__lowerCAmelCase		,    dtype=torch.floataa   )
      else:
          _a							:       int       					=			torch.from_numpy(__lowerCAmelCase   ).to(device=__lowerCAmelCase   )

      _a							:       Any       					=			[]



  def 						a_       ( self		,    __lowerCAmelCase		,    __lowerCAmelCase   ):







      '''simple docstring'''


      _a							:       Any       					=			np.log(__lowerCAmelCase   )

      # get distribution
      _a							:       Optional[Any]       					=			log_sigma - log_sigmas[:, np.newaxis]

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

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

      # interpolate sigmas
      _a							:       Union[str, Any]       					=			(low - log_sigma) / (low - high)
      _a							:       Tuple       					=			np.clip(__lowerCAmelCase		,    0		,    1   )

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



  def 						a_       ( self		,    __lowerCAmelCase   ):







      '''simple docstring'''


      _a							:       float       					=			in_sigmas[-1].item()
      _a							:       float       					=			in_sigmas[0].item()

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



  def 						a_       ( self		,    __lowerCAmelCase		,    __lowerCAmelCase		,    __lowerCAmelCase		,    __lowerCAmelCase = 4		,    __lowerCAmelCase = True		,    ):







      '''simple docstring'''


      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   ):
          _a							:       Tuple       					=			timestep.to(self.timesteps.device   )
      _a							:       List[str]       					=			(self.timesteps == timestep).nonzero().item()
      _a							:       str       					=			self.sigmas[step_index]

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

      # 3. Compute linear multistep coefficients
      _a							:       Optional[Any]       					=			min(step_index + 1		,    __lowerCAmelCase   )
      _a							:       int       					=			[self.get_lms_coefficient(__lowerCAmelCase		,    __lowerCAmelCase		,    __lowerCAmelCase   ) for curr_order in range(__lowerCAmelCase   )]

      # 4. Compute previous sample based on the derivatives path
      _a							:       Optional[Any]       					=			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 						a_       ( self		,    __lowerCAmelCase		,    __lowerCAmelCase		,    __lowerCAmelCase		,    ):







      '''simple docstring'''


      _a							:       Optional[Any]       					=			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
          _a							:       Any       					=			self.timesteps.to(original_samples.device		,    dtype=torch.floataa   )
          _a							:       Optional[Any]       					=			timesteps.to(original_samples.device		,    dtype=torch.floataa   )
      else:
          _a							:       int       					=			self.timesteps.to(original_samples.device   )
          _a							:       Optional[Any]       					=			timesteps.to(original_samples.device   )

      _a							:       Any       					=			[(schedule_timesteps == t).nonzero().item() for t in timesteps]

      _a							:       List[str]       					=			sigmas[step_indices].flatten()
      while len(sigma.shape   ) < len(original_samples.shape   ):
          _a							:       int       					=			sigma.unsqueeze(-1   )

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



  def __len__( self   ):







      '''simple docstring'''


      return self.config.num_train_timesteps


